helpcontent2/source/text/scalc/01/04060119.xhp

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  38 <topic id="textscalc0104060119xml" indexer="include">
  39 <title id="tit" xml-lang="en-US">Financial Functions Part Two</title>
  40 <filename>/text/scalc/01/04060119.xhp</filename>
  41 </topic>
  42 </meta>
  43 <body>
  44 <paragraph role="heading" id="hd_id3149052" xml-lang="en-US" level="1" l10n="U" oldref="1">Financial Functions Part Two</paragraph>
  45 <section id="howtoget">
  46 <embed href="text/scalc/00/00000404.xhp#eikafi"/>
  47 </section>
  48 <paragraph role="paragraph" id="par_id3148742" xml-lang="en-US" l10n="U" oldref="343"><link href="text/scalc/01/04060103.xhp" name="Back to Financial Functions Part One">Back to Financial Functions Part One</link></paragraph>
  49 <paragraph role="paragraph" id="par_id3151341" xml-lang="en-US" l10n="U" oldref="344"><link href="text/scalc/01/04060118.xhp" name="Forward to Financial Functions Part Three">Forward to Financial Functions Part Three</link></paragraph>
  50 <sort order="asc">
  51 <section id="ppmt">
  52 <bookmark xml-lang="en-US" branch="index" id="bm_id3150026"><bookmark_value>PPMT function</bookmark_value>
  53 </bookmark>
  54 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_KAPZ" id="bm_id3145827" localize="false"/>
  55 <paragraph role="heading" id="hd_id3150026" xml-lang="en-US" level="2" l10n="U" oldref="238">PPMT</paragraph>
  56 <paragraph role="paragraph" id="par_id3146942" xml-lang="en-US" l10n="U" oldref="239"><ahelp hid="HID_FUNC_KAPZ">Returns for a given period the payment on the principal for an investment that is based on periodic and constant payments and a constant interest rate.</ahelp></paragraph>
  57 <paragraph role="heading" id="hd_id3150459" xml-lang="en-US" level="3" l10n="U" oldref="240">Syntax</paragraph>
  58 <paragraph role="code" id="par_id3146878" xml-lang="en-US" l10n="U" oldref="241">PPMT(Rate; Period; NPer; PV; FV; Type)</paragraph>
  59 <paragraph role="paragraph" id="par_id3151228" xml-lang="en-US" l10n="U" oldref="242">
  60 <emph>Rate</emph> is the periodic interest rate.</paragraph>
  61 <paragraph role="paragraph" id="par_id3148887" xml-lang="en-US" l10n="U" oldref="243">
  62 <emph>Period</emph> is the amortizement period. P = 1 for the first and P = NPer for the last period.</paragraph>
  63 <paragraph role="paragraph" id="par_id3148436" xml-lang="en-US" l10n="U" oldref="244">
  64 <emph>NPer</emph> is the total number of periods during which annuity is paid.</paragraph>
  65 <paragraph role="paragraph" id="par_id3153035" xml-lang="en-US" l10n="U" oldref="245">
  66 <emph>PV</emph> is the present value in the sequence of payments.</paragraph>
  67 <paragraph role="paragraph" id="par_id3147474" xml-lang="en-US" l10n="U" oldref="246">
  68 <emph>FV</emph> (optional) is the desired (future) value.</paragraph>
  69 <paragraph role="paragraph" id="par_id3144744" xml-lang="en-US" l10n="U" oldref="247">
  70 <emph>Type</emph> (optional) defines the due date. F = 1 for payment at the beginning of a period and F = 0 for payment at the end of a period.</paragraph>
  71 <paragraph role="paragraph" id="par_idN1067C" xml-lang="en-US" l10n="NEW">
  72 <embedvar href="text/scalc/00/00000004.xhp#optional"/>
  73 </paragraph>
  74 <paragraph role="heading" id="hd_id3148582" xml-lang="en-US" level="3" l10n="U" oldref="248">Example</paragraph>
  75 <paragraph role="paragraph" id="par_id3154811" xml-lang="en-US" l10n="CHG" oldref="249">How high is the periodic monthly payment at an annual interest rate of 8.75% over a period of 3 years? The cash value is 5,000 currency units and is always paid at the beginning of a period. The future value is 8,000 currency units.</paragraph>
  76 <paragraph role="paragraph" id="par_id3149246" xml-lang="en-US" l10n="U" oldref="250">
  77 <item type="input">=PPMT(8.75%/12;1;36;5000;8000;1)</item> = -350.99 currency units.</paragraph>
  78 </section>
  79 <section id="cumprinc">
  80 <bookmark xml-lang="en-US" branch="index" id="bm_id3146139"><bookmark_value>calculating; total amortizement rates</bookmark_value>
  81 <bookmark_value>total amortizement rates</bookmark_value>
  82 <bookmark_value>amortization installment</bookmark_value>
  83 <bookmark_value>repayment installment</bookmark_value>
  84 <bookmark_value>CUMPRINC function</bookmark_value>
  85 </bookmark><comment>mw added two entries</comment>
  86 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_KUMKAPITAL" id="bm_id3148754" localize="false"/>
  87 <paragraph role="heading" id="hd_id3146139" xml-lang="en-US" level="2" oldref="252">CUMPRINC</paragraph>
  88 <paragraph role="paragraph" id="par_id3150140" xml-lang="en-US" l10n="U" oldref="253"><ahelp hid="HID_FUNC_KUMKAPITAL">Returns the cumulative interest paid for an investment period with a constant interest rate.</ahelp></paragraph>
  89 <paragraph role="heading" id="hd_id3149188" xml-lang="en-US" level="3" l10n="U" oldref="254">Syntax</paragraph>
  90 <paragraph role="code" id="par_id3148733" xml-lang="en-US" l10n="U" oldref="255">CUMPRINC(Rate; NPer; PV; S; E; Type)</paragraph>
  91 <paragraph role="paragraph" id="par_id3150864" xml-lang="en-US" l10n="U" oldref="256">
  92 <emph>Rate</emph> is the periodic interest rate.</paragraph>
  93 <paragraph role="paragraph" id="par_id3166052" xml-lang="en-US" l10n="U" oldref="257">
  94 <emph>NPer</emph> is the payment period with the total number of periods. NPER can also be a non-integer value.</paragraph>
  95 <paragraph role="paragraph" id="par_id3150007" xml-lang="en-US" l10n="U" oldref="258">
  96 <emph>PV</emph> is the current value in the sequence of payments.</paragraph>
  97 <paragraph role="paragraph" id="par_id3153112" xml-lang="en-US" l10n="U" oldref="259">
  98 <emph>S</emph> is the first period.</paragraph>
  99 <paragraph role="paragraph" id="par_id3146847" xml-lang="en-US" l10n="U" oldref="260">
 100 <emph>E</emph> is the last period.</paragraph>
 101 <paragraph role="paragraph" id="par_id3145167" xml-lang="en-US" l10n="U" oldref="261">
 102 <emph>Type</emph> is the due date of the payment at the beginning or end of each period.</paragraph>
 103 <paragraph role="heading" id="hd_id3154502" xml-lang="en-US" level="3" l10n="U" oldref="262">Example</paragraph>
 104 <paragraph role="paragraph" id="par_id3153570" xml-lang="en-US" l10n="U" oldref="263">What are the payoff amounts if the yearly interest rate is 5.5% for 36 months? The cash value is 15,000 currency units. The payoff amount is calculated between the 10th and 18th period. The due date is at the end of the period.</paragraph>
 105 <paragraph role="paragraph" id="par_id3149884" xml-lang="en-US" l10n="U" oldref="264">
 106 <item type="input">=CUMPRINC(5.5%/12;36;15000;10;18;0)</item> = -3669.74 currency units. The payoff amount between the 10th and 18th period is 3669.74 currency units.</paragraph>
 107 </section>
 108 <section id="cumprinc_add">
 109 <bookmark xml-lang="en-US" branch="index" id="bm_id3150019"><bookmark_value>CUMPRINC_ADD function</bookmark_value>
 110 </bookmark>
 111 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_CUMPRINC" id="bm_id3154330" localize="false"/>
 112 <paragraph role="heading" id="hd_id3150019" xml-lang="en-US" level="2" oldref="182">CUMPRINC_ADD</paragraph>
 113 <paragraph role="paragraph" id="par_id3145246" xml-lang="en-US" l10n="U" oldref="183"><ahelp hid="HID_AAI_FUNC_CUMPRINC"> Calculates the cumulative redemption of a loan in a period.</ahelp></paragraph>
 114 <embed href="text/scalc/01/04060102.xhp#ADD_note"/>
 115 <paragraph role="heading" id="hd_id3153047" xml-lang="en-US" level="3" l10n="U" oldref="184">Syntax</paragraph>
 116 <paragraph role="code" id="par_id3157970" xml-lang="en-US" l10n="U" oldref="185">CUMPRINC_ADD(Rate; NPer; PV; StartPeriod; EndPeriod; Type)</paragraph>
 117 <paragraph role="paragraph" id="par_id3145302" xml-lang="en-US" l10n="U" oldref="186">
 118 <emph>Rate</emph> is the interest rate for each period.</paragraph>
 119 <paragraph role="paragraph" id="par_id3151017" xml-lang="en-US" l10n="U" oldref="187">
 120 <emph>NPer</emph> is the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly.</paragraph>
 121 <paragraph role="paragraph" id="par_id3155620" xml-lang="en-US" l10n="U" oldref="188">
 122 <emph>PV</emph> is the current value.</paragraph>
 123 <paragraph role="paragraph" id="par_id3145352" xml-lang="en-US" l10n="U" oldref="189">
 124 <emph>StartPeriod</emph> is the first payment period for the calculation.</paragraph>
 125 <paragraph role="paragraph" id="par_id3157986" xml-lang="en-US" l10n="U" oldref="190">
 126 <emph>EndPeriod</emph> is the last payment period for the calculation.</paragraph>
 127 <paragraph role="paragraph" id="par_id3150570" xml-lang="en-US" l10n="U" oldref="191">
 128 <emph>Type</emph> is the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).</paragraph>
 129 <paragraph role="heading" id="hd_id3150269" xml-lang="en-US" level="3" l10n="U" oldref="192">Example</paragraph>
 130 <paragraph role="paragraph" id="par_id3148774" xml-lang="en-US" l10n="U" oldref="193">The following mortgage loan is taken out on a house:</paragraph>
 131 <paragraph role="paragraph" id="par_id3150661" xml-lang="en-US" l10n="U" oldref="194">Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (payment periods = 30 * 12 = 360), NPV: 125000 currency units.</paragraph>
 132 <paragraph role="paragraph" id="par_id3155512" xml-lang="en-US" l10n="U" oldref="195">How much will you repay in the second year of the mortgage (thus from periods 13 to 24)?</paragraph>
 133 <paragraph role="paragraph" id="par_id3149394" xml-lang="en-US" l10n="U" oldref="196">
 134 <item type="input">=CUMPRINC_ADD(0.0075;360;125000;13;24;0)</item> returns -934.1071</paragraph>
 135 <paragraph role="paragraph" id="par_id3149026" xml-lang="en-US" l10n="U" oldref="197">In the first month you will be repaying the following amount:</paragraph>
 136 <paragraph role="paragraph" id="par_id3154636" xml-lang="en-US" l10n="U" oldref="198">
 137 <item type="input">=CUMPRINC_ADD(0.0075;360;125000;1;1;0)</item> returns -68.27827</paragraph>
 138 </section>
 139 <section id="cumipmt">
 140 <bookmark xml-lang="en-US" branch="index" id="bm_id3155370"><bookmark_value>calculating; accumulated interests</bookmark_value>
 141 <bookmark_value>accumulated interests</bookmark_value>
 142 <bookmark_value>CUMIPMT function</bookmark_value>
 143 </bookmark>
 144 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_KUMZINSZ" id="bm_id3148593" localize="false"/>
 145 <paragraph role="heading" id="hd_id3155370" xml-lang="en-US" level="2" oldref="266">CUMIPMT</paragraph>
 146 <paragraph role="paragraph" id="par_id3158411" xml-lang="en-US" l10n="U" oldref="267"><ahelp hid="HID_FUNC_KUMZINSZ">Calculates the cumulative interest payments, that is, the total interest, for an investment based on a constant interest rate.</ahelp></paragraph>
 147 <paragraph role="heading" id="hd_id3155814" xml-lang="en-US" level="3" l10n="U" oldref="268">Syntax</paragraph>
 148 <paragraph role="code" id="par_id3147536" xml-lang="en-US" l10n="U" oldref="269">CUMIPMT(Rate; NPer; PV; S; E; Type)</paragraph>
 149 <paragraph role="paragraph" id="par_id3150475" xml-lang="en-US" l10n="U" oldref="270">
 150 <emph>Rate</emph> is the periodic interest rate.</paragraph>
 151 <paragraph role="paragraph" id="par_id3153921" xml-lang="en-US" l10n="U" oldref="271">
 152 <emph>NPer</emph> is the payment period with the total number of periods. NPER can also be a non-integer value.</paragraph>
 153 <paragraph role="paragraph" id="par_id3153186" xml-lang="en-US" l10n="U" oldref="272">
 154 <emph>PV</emph> is the current value in the sequence of payments.</paragraph>
 155 <paragraph role="paragraph" id="par_id3156259" xml-lang="en-US" l10n="U" oldref="273">
 156 <emph>S</emph> is the first period.</paragraph>
 157 <paragraph role="paragraph" id="par_id3155990" xml-lang="en-US" l10n="U" oldref="274">
 158 <emph>E</emph> is the last period.</paragraph>
 159 <paragraph role="paragraph" id="par_id3149777" xml-lang="en-US" l10n="U" oldref="275">
 160 <emph>Type</emph> is the due date of the payment at the beginning or end of each period.</paragraph>
 161 <paragraph role="heading" id="hd_id3153723" xml-lang="en-US" level="3" l10n="U" oldref="276">Example</paragraph>
 162 <paragraph role="paragraph" id="par_id3147478" xml-lang="en-US" l10n="U" oldref="277">What are the interest payments at a yearly interest rate of 5.5 %, a payment period of monthly payments for 2 years and a current cash value of 5,000 currency units? The start period is the 4th and the end period is the 6th period. The payment is due at the beginning of each period.</paragraph>
 163 <paragraph role="paragraph" id="par_id3149819" xml-lang="en-US" l10n="U" oldref="278">
 164 <item type="input">=CUMIPMT(5.5%/12;24;5000;4;6;1)</item> = -57.54 currency units. The interest payments for between the 4th and 6th period are 57.54 currency units.</paragraph>
 165 </section>
 166 <section id="cumipmt_add">
 167 <bookmark xml-lang="en-US" branch="index" id="bm_id3083280"><bookmark_value>CUMIPMT_ADD function</bookmark_value>
 168 </bookmark>
 169 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_CUMIPMT" id="bm_id3154312" localize="false"/>
 170 <paragraph role="heading" id="hd_id3083280" xml-lang="en-US" level="2" oldref="165">CUMIPMT_ADD</paragraph>
 171 <paragraph role="paragraph" id="par_id3152482" xml-lang="en-US" l10n="U" oldref="166"><ahelp hid="HID_AAI_FUNC_CUMIPMT">Calculates the accumulated interest for a period.</ahelp></paragraph>
 172 <embed href="text/scalc/01/04060102.xhp#ADD_note"/>
 173 <paragraph role="heading" id="hd_id3149713" xml-lang="en-US" level="3" l10n="U" oldref="167">Syntax</paragraph>
 174 <paragraph role="code" id="par_id3145087" xml-lang="en-US" l10n="U" oldref="168">CUMIPMT_ADD(Rate; NPer; PV; StartPeriod; EndPeriod; Type)</paragraph>
 175 <paragraph role="paragraph" id="par_id3149277" xml-lang="en-US" l10n="U" oldref="169">
 176 <emph>Rate</emph> is the interest rate for each period.</paragraph>
 177 <paragraph role="paragraph" id="par_id3149270" xml-lang="en-US" l10n="U" oldref="170">
 178 <emph>NPer</emph> is the total number of payment periods. The rate and NPER must refer to the same unit, and thus both be calculated annually or monthly.</paragraph>
 179 <paragraph role="paragraph" id="par_id3152967" xml-lang="en-US" l10n="U" oldref="171">
 180 <emph>PV</emph> is the current value.</paragraph>
 181 <paragraph role="paragraph" id="par_id3156308" xml-lang="en-US" l10n="U" oldref="172">
 182 <emph>StartPeriod</emph> is the first payment period for the calculation.</paragraph>
 183 <paragraph role="paragraph" id="par_id3149453" xml-lang="en-US" l10n="U" oldref="173">
 184 <emph>EndPeriod</emph> is the last payment period for the calculation.</paragraph>
 185 <paragraph role="paragraph" id="par_id3150962" xml-lang="en-US" l10n="U" oldref="174">
 186 <emph>Type</emph> is the maturity of a payment at the end of each period (Type = 0) or at the start of the period (Type = 1).</paragraph>
 187 <paragraph role="heading" id="hd_id3152933" xml-lang="en-US" level="3" l10n="U" oldref="175">Example</paragraph>
 188 <paragraph role="paragraph" id="par_id3156324" xml-lang="en-US" l10n="U" oldref="176">The following mortgage loan is taken out on a house:</paragraph>
 189 <paragraph role="paragraph" id="par_id3147566" xml-lang="en-US" l10n="U" oldref="177">Rate: 9.00 per cent per annum (9% / 12 = 0.0075), Duration: 30 years (NPER = 30 * 12 = 360), Pv: 125000 currency units.</paragraph>
 190 <paragraph role="paragraph" id="par_id3151272" xml-lang="en-US" l10n="U" oldref="178">How much interest must you pay in the second year of the mortgage (thus from periods 13 to 24)?</paragraph>
 191 <paragraph role="paragraph" id="par_id3156130" xml-lang="en-US" l10n="U" oldref="179">
 192 <item type="input">=CUMIPMT_ADD(0.0075;360;125000;13;24;0)</item> returns -11135.23.</paragraph>
 193 <paragraph role="paragraph" id="par_id3150764" xml-lang="en-US" l10n="U" oldref="180">How much interest must you pay in the first month?</paragraph>
 194 <paragraph role="paragraph" id="par_id3146857" xml-lang="en-US" l10n="U" oldref="181">
 195 <item type="input">=CUMIPMT_ADD(0.0075;360;125000;1;1;0)</item> returns -937.50.</paragraph>
 196 </section>
 197 <section id="price">
 198 <bookmark xml-lang="en-US" branch="index" id="bm_id3150878"><bookmark_value>PRICE function</bookmark_value>
 199 <bookmark_value>prices; fixed interest securities</bookmark_value>
 200 <bookmark_value>sales values;fixed interest securities</bookmark_value>
 201 </bookmark><comment>mw added two entries</comment>
 202 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_PRICE" id="bm_id3153279" localize="false"/>
 203 <paragraph role="heading" id="hd_id3150878" xml-lang="en-US" level="2" oldref="9">PRICE</paragraph>
 204 <paragraph role="paragraph" id="par_id3153210" xml-lang="en-US" l10n="U" oldref="10"><ahelp hid="HID_AAI_FUNC_PRICE">Calculates the market value of a fixed interest security with a par value of 100 currency units as a function of the forecast yield.</ahelp></paragraph>
 205 <paragraph role="heading" id="hd_id3154646" xml-lang="en-US" level="3" l10n="U" oldref="11">Syntax</paragraph>
 206 <paragraph role="code" id="par_id3152804" xml-lang="en-US" l10n="U" oldref="12">PRICE(Settlement; Maturity; Rate; Yield; Redemption; Frequency; Basis)</paragraph>
 207 <paragraph role="paragraph" id="par_id3156121" xml-lang="en-US" l10n="U" oldref="13">
 208 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 209 <paragraph role="paragraph" id="par_id3149983" xml-lang="en-US" l10n="U" oldref="14">
 210 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 211 <paragraph role="paragraph" id="par_id3153755" xml-lang="en-US" l10n="U" oldref="15">
 212 <emph>Rate</emph> is the annual nominal rate of interest (coupon interest rate)</paragraph>
 213 <paragraph role="paragraph" id="par_id3155999" xml-lang="en-US" l10n="U" oldref="16">
 214 <emph>Yield</emph> is the annual yield of the security.</paragraph>
 215 <paragraph role="paragraph" id="par_id3156114" xml-lang="en-US" l10n="U" oldref="17">
 216 <emph>Redemption</emph> is the redemption value per 100 currency units of par value.</paragraph>
 217 <paragraph role="paragraph" id="par_id3155846" xml-lang="en-US" l10n="U" oldref="18">
 218 <emph>Frequency</emph> is the number of interest payments per year (1, 2 or 4).</paragraph>
 219 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 220 <paragraph role="heading" id="hd_id3153148" xml-lang="en-US" level="3" l10n="U" oldref="19">Example</paragraph>
 221 <paragraph role="paragraph" id="par_id3150260" xml-lang="en-US" l10n="CHG" oldref="20">A security is purchased on 1999-02-15; the maturity date is 2007-11-15. The nominal rate of interest is 5.75%. The yield is 6.5%. The redemption value is 100 currency units. Interest is paid half-yearly (frequency is 2). With calculation on basis 0, the price is as follows:</paragraph>
 222 <paragraph role="paragraph" id="par_id3147273" xml-lang="en-US" l10n="CHG" oldref="21">=PRICE("1999-02-15"; "2007-11-15"; 0.0575; 0.065; 100; 2; 0) returns 95.04287.</paragraph>
 223 </section>
 224 <section id="pricedisc">
 225 <bookmark xml-lang="en-US" branch="index" id="bm_id3151297"><bookmark_value>PRICEDISC function</bookmark_value>
 226 <bookmark_value>prices;non-interest-bearing securities</bookmark_value>
 227 <bookmark_value>sales values;non-interest-bearing securities</bookmark_value>
 228 </bookmark><comment>mw added two entries</comment>
 229 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_PRICEDISC" id="bm_id3143236" localize="false"/>
 230 <paragraph role="heading" id="hd_id3151297" xml-lang="en-US" level="2" oldref="22">PRICEDISC</paragraph>
 231 <paragraph role="paragraph" id="par_id3155100" xml-lang="en-US" l10n="U" oldref="23"><ahelp hid="HID_AAI_FUNC_PRICEDISC">Calculates the price per 100 currency units of par value of a non-interest- bearing security.</ahelp></paragraph>
 232 <paragraph role="heading" id="hd_id3149294" xml-lang="en-US" level="3" l10n="U" oldref="24">Syntax</paragraph>
 233 <paragraph role="code" id="par_id3146084" xml-lang="en-US" l10n="U" oldref="25">PRICEDISC(Settlement; Maturity; Discount; Redemption; Basis)</paragraph>
 234 <paragraph role="paragraph" id="par_id3159179" xml-lang="en-US" l10n="U" oldref="26">
 235 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 236 <paragraph role="paragraph" id="par_id3154304" xml-lang="en-US" l10n="U" oldref="27">
 237 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 238 <paragraph role="paragraph" id="par_id3156014" xml-lang="en-US" l10n="U" oldref="28">
 239 <emph>Discount</emph> is the discount of a security as a percentage.</paragraph>
 240 <paragraph role="paragraph" id="par_id3147489" xml-lang="en-US" l10n="U" oldref="29">
 241 <emph>Redemption</emph> is the redemption value per 100 currency units of par value.</paragraph>
 242 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 243 <paragraph role="heading" id="hd_id3152794" xml-lang="en-US" level="3" l10n="U" oldref="30">Example</paragraph>
 244 <paragraph role="paragraph" id="par_id3149198" xml-lang="en-US" l10n="CHG" oldref="31">A security is purchased on 1999-02-15; the maturity date is 1999-03-01. Discount in per cent is 5.25%. The redemption value is 100. When calculating on basis 2 the price discount is as follows:</paragraph>
 245 <paragraph role="paragraph" id="par_id3151178" xml-lang="en-US" l10n="CHG" oldref="32">=PRICEDISC("1999-02-15"; "1999-03-01"; 0.0525; 100; 2) returns 99.79583.</paragraph>
 246 </section>
 247 <section id="pricemat">
 248 <bookmark xml-lang="en-US" branch="index" id="bm_id3154693"><bookmark_value>PRICEMAT function</bookmark_value>
 249 <bookmark_value>prices;interest-bearing securities</bookmark_value>
 250 </bookmark><comment>mw added one entry</comment>
 251 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_PRICEMAT" id="bm_id3150118" localize="false"/>
 252 <paragraph role="heading" id="hd_id3154693" xml-lang="en-US" level="2" oldref="33">PRICEMAT</paragraph>
 253 <paragraph role="paragraph" id="par_id3153906" xml-lang="en-US" l10n="U" oldref="34"><ahelp hid="HID_AAI_FUNC_PRICEMAT">Calculates the price per 100 currency units of par value of a security, that pays interest on the maturity date.</ahelp></paragraph>
 254 <paragraph role="heading" id="hd_id3154933" xml-lang="en-US" level="3" l10n="U" oldref="35">Syntax</paragraph>
 255 <paragraph role="code" id="par_id3155393" xml-lang="en-US" l10n="U" oldref="36">PRICEMAT(Settlement; Maturity; Issue; Rate; Yield; Basis)</paragraph>
 256 <paragraph role="paragraph" id="par_id3153102" xml-lang="en-US" l10n="U" oldref="37">
 257 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 258 <paragraph role="paragraph" id="par_id3150530" xml-lang="en-US" l10n="U" oldref="38">
 259 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 260 <paragraph role="paragraph" id="par_id3149903" xml-lang="en-US" l10n="U" oldref="39">
 261 <emph>Issue</emph> is the date of issue of the security.</paragraph>
 262 <paragraph role="paragraph" id="par_id3148828" xml-lang="en-US" l10n="U" oldref="40">
 263 <emph>Rate</emph> is the interest rate of the security on the issue date.</paragraph>
 264 <paragraph role="paragraph" id="par_id3146993" xml-lang="en-US" l10n="U" oldref="41">
 265 <emph>Yield</emph> is the annual yield of the security.</paragraph>
 266 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 267 <paragraph role="heading" id="hd_id3150507" xml-lang="en-US" level="3" l10n="U" oldref="42">Example</paragraph>
 268 <paragraph role="paragraph" id="par_id3154289" xml-lang="en-US" l10n="U" oldref="43">Settlement date: February 15 1999, maturity date: April 13 1999, issue date: November 11 1998. Interest rate: 6.1 per cent, yield: 6.1 per cent, basis: 30/360 = 0.</paragraph>
 269 <paragraph role="paragraph" id="par_id3154905" xml-lang="en-US" l10n="U" oldref="44">The price is calculated as follows:</paragraph>
 270 <paragraph role="paragraph" id="par_id3158409" xml-lang="en-US" l10n="CHG" oldref="45">=PRICEMAT("1999-02-15";"1999-04-13";"1998-11-11"; 0.061; 0.061;0) returns 99.98449888.</paragraph>
 271 </section>
 272 <section id="duration">
 273 <bookmark xml-lang="en-US" branch="index" id="bm_id3148448"><bookmark_value>calculating; durations</bookmark_value>
 274 <bookmark_value>durations;calculating</bookmark_value>
 275 <bookmark_value>DURATION function</bookmark_value>
 276 </bookmark>
 277 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_LAUFZEIT" id="bm_id3154208" localize="false"/>
 278 <paragraph role="heading" id="hd_id3148448" xml-lang="en-US" level="2" l10n="U" oldref="280">DURATION</paragraph>
 279 <paragraph role="paragraph" id="par_id3153056" xml-lang="en-US" l10n="CHG" oldref="281"><ahelp hid="HID_FUNC_LAUFZEIT">Calculates the number of periods required by an investment to attain the desired value.</ahelp></paragraph>
 280 <paragraph role="heading" id="hd_id3145421" xml-lang="en-US" level="3" l10n="U" oldref="282">Syntax</paragraph>
 281 <paragraph role="code" id="par_id3148933" xml-lang="en-US" l10n="U" oldref="283">DURATION(Rate; PV; FV)</paragraph>
 282 <paragraph role="paragraph" id="par_id3148801" xml-lang="en-US" l10n="U" oldref="284">
 283 <emph>Rate</emph> is a constant. The interest rate is to be calculated for the entire duration (duration period). The interest rate per period is calculated by dividing the interest rate by the calculated duration. The internal rate for an annuity is to be entered as Rate/12.</paragraph>
 284 <paragraph role="paragraph" id="par_id3147239" xml-lang="en-US" l10n="U" oldref="285">
 285 <emph>PV</emph> is the present (current) value. The cash value is the deposit of cash or the current cash value of an allowance in kind. As a deposit value a positive value must be entered; the deposit must not be 0 or &lt;0.</paragraph>
 286 <paragraph role="paragraph" id="par_id3147515" xml-lang="en-US" l10n="U" oldref="286">
 287 <emph>FV</emph> is the expected value. The future value determines the desired (future) value of the deposit.</paragraph>
 288 <paragraph role="heading" id="hd_id3153579" xml-lang="en-US" level="3" l10n="U" oldref="287">Example</paragraph>
 289 <paragraph role="paragraph" id="par_id3148480" xml-lang="en-US" l10n="U" oldref="288">At an interest rate of 4.75%, a cash value of 25,000 currency units and a future value of 1,000,000 currency units, a duration of 79.49 payment periods is returned. The periodic payment is the resulting quotient from the future value and the duration, in this case 1,000,000/79.49=12,850.20.</paragraph>
 290 </section>
 291 <section id="sln">
 292 <bookmark xml-lang="en-US" branch="index" id="bm_id3148912"><bookmark_value>calculating;linear depreciations</bookmark_value>
 293 <bookmark_value>depreciations;linear</bookmark_value>
 294 <bookmark_value>linear depreciations</bookmark_value>
 295 <bookmark_value>straight-line depreciations</bookmark_value>
 296 <bookmark_value>SLN function</bookmark_value>
 297 </bookmark><comment>mw added one entry</comment>
 298 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_LIA" id="bm_id3154275" localize="false"/>
 299 <paragraph role="heading" id="hd_id3148912" xml-lang="en-US" level="2" l10n="U" oldref="290">SLN</paragraph>
 300 <paragraph role="paragraph" id="par_id3149154" xml-lang="en-US" l10n="U" oldref="291"><ahelp hid="HID_FUNC_LIA">Returns the straight-line depreciation of an asset for one period.</ahelp>The amount of the depreciation is constant during the depreciation period.</paragraph>
 301 <paragraph role="heading" id="hd_id3153240" xml-lang="en-US" level="3" l10n="U" oldref="292">Syntax</paragraph>
 302 <paragraph role="code" id="par_id3166456" xml-lang="en-US" l10n="U" oldref="293">SLN(Cost; Salvage; Life)</paragraph>
 303 <paragraph role="paragraph" id="par_id3146955" xml-lang="en-US" l10n="U" oldref="294">
 304 <emph>Cost</emph> is the initial cost of an asset.</paragraph>
 305 <paragraph role="paragraph" id="par_id3149796" xml-lang="en-US" l10n="U" oldref="295">
 306 <emph>Salvage</emph> is the value of an asset at the end of the depreciation.</paragraph>
 307 <paragraph role="paragraph" id="par_id3166444" xml-lang="en-US" l10n="U" oldref="296">
 308 <emph>Life</emph> is the depreciation period determining the number of periods in the depreciation of the asset.</paragraph>
 309 <paragraph role="heading" id="hd_id3155579" xml-lang="en-US" level="3" l10n="U" oldref="297">Example</paragraph>
 310 <paragraph role="paragraph" id="par_id3154098" xml-lang="en-US" l10n="U" oldref="298">Office equipment with an initial cost of 50,000 currency units is to be depreciated over 7 years. The value at the end of the depreciation is to be 3,500 currency units.</paragraph>
 311 <paragraph role="paragraph" id="par_id3153390" xml-lang="en-US" l10n="U" oldref="299">
 312 <item type="input">=SLN(50000;3,500;84)</item> = 553.57 currency units. The periodic monthly depreciation of the office equipment is 553.57 currency units.</paragraph>
 313 </section>
 314 <section id="mduration">
 315 <bookmark xml-lang="en-US" branch="index" id="bm_id3153739"><bookmark_value>MDURATION function</bookmark_value>
 316 <bookmark_value>Macauley duration</bookmark_value>
 317 </bookmark><comment>mw added one entry</comment>
 318 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_MDURATION" id="bm_id3153750" localize="false"/>
 319 <paragraph role="heading" id="hd_id3153739" xml-lang="en-US" level="2" oldref="217">MDURATION</paragraph>
 320 <paragraph role="paragraph" id="par_id3149923" xml-lang="en-US" l10n="U" oldref="218"><ahelp hid="HID_AAI_FUNC_MDURATION">Calculates the modified Macauley duration of a fixed interest security in years.</ahelp></paragraph>
 321 <paragraph role="heading" id="hd_id3149964" xml-lang="en-US" level="3" l10n="U" oldref="219">Syntax</paragraph>
 322 <paragraph role="code" id="par_id3148987" xml-lang="en-US" l10n="U" oldref="220">MDURATION(Settlement; Maturity; Coupon; Yield; Frequency; Basis)</paragraph>
 323 <paragraph role="paragraph" id="par_id3148619" xml-lang="en-US" l10n="U" oldref="221">
 324 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 325 <paragraph role="paragraph" id="par_id3149805" xml-lang="en-US" l10n="U" oldref="222">
 326 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 327 <paragraph role="paragraph" id="par_id3154338" xml-lang="en-US" l10n="U" oldref="223">
 328 <emph>Coupon</emph> is the annual nominal rate of interest (coupon interest rate)</paragraph>
 329 <paragraph role="paragraph" id="par_id3148466" xml-lang="en-US" l10n="U" oldref="224">
 330 <emph>Yield</emph> is the annual yield of the security.</paragraph>
 331 <paragraph role="paragraph" id="par_id3149423" xml-lang="en-US" l10n="U" oldref="225">
 332 <emph>Frequency</emph> is the number of interest payments per year (1, 2 or 4).</paragraph>
 333 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 334 <paragraph role="heading" id="hd_id3154602" xml-lang="en-US" level="3" l10n="U" oldref="226">Example</paragraph>
 335 <paragraph role="paragraph" id="par_id3148652" xml-lang="en-US" l10n="CHG" oldref="227">A security is purchased on 2001-01-01; the maturity date is 2006-01-01. The nominal rate of interest is 8%. The yield is 9.0%. Interest is paid half-yearly (frequency is 2). Using daily balance interest calculation (basis 3) how long is the modified duration?</paragraph>
 336 <paragraph role="paragraph" id="par_id3145378" xml-lang="en-US" l10n="CHG" oldref="228">=MDURATION("2001-01-01"; "2006-01-01"; 0.08; 0.09; 2; 3) returns 4.02 years.</paragraph>
 337 </section>
 338 <section id="npv">
 339 <bookmark xml-lang="en-US" branch="index" id="bm_id3149242"><bookmark_value>calculating;net present values</bookmark_value>
 340 <bookmark_value>net present values</bookmark_value>
 341 <bookmark_value>NPV function</bookmark_value>
 342 </bookmark>
 343 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_NBW" id="bm_id3148417" localize="false"/>
 344 <paragraph role="heading" id="hd_id3149242" xml-lang="en-US" level="2" l10n="U" oldref="301">NPV</paragraph>
 345 <paragraph role="paragraph" id="par_id3145308" xml-lang="en-US" l10n="CHG" oldref="302"><ahelp hid="HID_FUNC_NBW">Returns the present value of an investment based on a series of periodic cash flows and a discount rate. To get the net present value, subtract the cost of the project (the initial cash flow at time zero) from the returned value.</ahelp></paragraph>
 346 <paragraph role="heading" id="hd_id3149937" xml-lang="en-US" level="3" l10n="U" oldref="303">Syntax</paragraph>
 347 <paragraph role="code" id="par_id3153321" xml-lang="en-US" l10n="U" oldref="304">NPV(Rate; Value1; Value2; ...)</paragraph>
 348 <paragraph role="paragraph" id="par_id3150630" xml-lang="en-US" l10n="U" oldref="305">
 349 <emph>Rate</emph> is the discount rate for a period.</paragraph>
 350 <paragraph role="paragraph" id="par_id3150427" xml-lang="en-US" l10n="U" oldref="306">
 351 <emph>Value1;...</emph> are up to 30 values, which represent deposits or withdrawals.</paragraph>
 352 <paragraph role="heading" id="hd_id3153538" xml-lang="en-US" level="3" l10n="U" oldref="307">Example</paragraph>
 353 <paragraph role="paragraph" id="par_id3154800" xml-lang="en-US" l10n="CHG" oldref="308">What is the net present value of periodic payments of 10, 20 and 30 currency units with a discount rate of 8.75%. At time zero the costs were payed as -40 currency units.</paragraph>
 354 <paragraph role="paragraph" id="par_id3143270" xml-lang="en-US" l10n="CHG" oldref="309">
 355 <item type="input">=NPV(8.75%;10;20;30)</item> = 49.43 currency units. The net present value is the returned value minus the initial costs of 40 currency units, therefore 9.43 currency units.</paragraph>
 356 </section>
 357 <section id="nominal">
 358 <bookmark xml-lang="en-US" branch="index" id="bm_id3149484"><bookmark_value>calculating;nominal interest rates</bookmark_value>
 359 <bookmark_value>nominal interest rates</bookmark_value>
 360 <bookmark_value>NOMINAL function</bookmark_value>
 361 </bookmark><comment>mw made "nominal interest rates;..." a one level entry</comment>
 362 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_NOMINAL" id="bm_id3145600" localize="false"/>
 363 <paragraph role="heading" id="hd_id3149484" xml-lang="en-US" level="2" l10n="U" oldref="311">NOMINAL</paragraph>
 364 <paragraph role="paragraph" id="par_id3149596" xml-lang="en-US" l10n="U" oldref="312"><ahelp hid="HID_FUNC_NOMINAL">Calculates the yearly nominal interest rate, given the effective rate and the number of compounding periods per year.</ahelp></paragraph>
 365 <paragraph role="heading" id="hd_id3151252" xml-lang="en-US" level="3" l10n="U" oldref="313">Syntax</paragraph>
 366 <paragraph role="code" id="par_id3152769" xml-lang="en-US" l10n="U" oldref="314">NOMINAL(EffectiveRate; NPerY)</paragraph>
 367 <paragraph role="paragraph" id="par_id3147521" xml-lang="en-US" l10n="U" oldref="315">
 368 <emph>EffectiveRate</emph> is the effective interest rate</paragraph>
 369 <paragraph role="paragraph" id="par_id3156334" xml-lang="en-US" l10n="U" oldref="316">
 370 <emph>NPerY</emph> is the number of periodic interest payments per year.</paragraph>
 371 <paragraph role="heading" id="hd_id3154473" xml-lang="en-US" level="3" l10n="U" oldref="317">Example</paragraph>
 372 <paragraph role="paragraph" id="par_id3147091" xml-lang="en-US" l10n="U" oldref="318">What is the nominal interest per year for an effective interest rate of 13.5% if twelve payments are made per year.</paragraph>
 373 <paragraph role="paragraph" id="par_id3154831" xml-lang="en-US" l10n="U" oldref="319">
 374 <item type="input">=NOMINAL(13.5%;12)</item> = 12.73%. The nominal interest rate per year is 12.73%.</paragraph>
 375 </section>
 376 <section id="nominal_add">
 377 <bookmark xml-lang="en-US" branch="index" id="bm_id3155123"><bookmark_value>NOMINAL_ADD function</bookmark_value>
 378 </bookmark>
 379 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_NOMINAL" id="bm_id3158439" localize="false"/>
 380 <paragraph role="heading" id="hd_id3155123" xml-lang="en-US" level="2" oldref="229">NOMINAL_ADD</paragraph>
 381 <paragraph role="paragraph" id="par_id3148671" xml-lang="en-US" l10n="U" oldref="230"><ahelp hid="HID_AAI_FUNC_NOMINAL">Calculates the annual nominal rate of interest on the basis of the effective rate and the number of interest payments per annum.</ahelp></paragraph>
 382 <embed href="text/scalc/01/04060102.xhp#ADD_note"/>
 383 <paragraph role="heading" id="hd_id3155611" xml-lang="en-US" level="3" l10n="U" oldref="231">Syntax</paragraph>
 384 <paragraph role="code" id="par_id3156157" xml-lang="en-US" l10n="U" oldref="232">NOMINAL_ADD(EffectiveRate; NPerY)</paragraph>
 385 <paragraph role="paragraph" id="par_id3153777" xml-lang="en-US" l10n="U" oldref="233">
 386 <emph>EffectiveRate</emph> is the effective annual rate of interest.</paragraph>
 387 <paragraph role="paragraph" id="par_id3150409" xml-lang="en-US" l10n="U" oldref="234">
 388 <emph>NPerY</emph> the number of interest payments per year.</paragraph>
 389 <paragraph role="heading" id="hd_id3146789" xml-lang="en-US" level="3" l10n="U" oldref="235">Example</paragraph>
 390 <paragraph role="paragraph" id="par_id3145777" xml-lang="en-US" l10n="U" oldref="236">What is the nominal rate of interest for a 5.3543% effective rate of interest and quarterly payment.</paragraph>
 391 <paragraph role="paragraph" id="par_id3156146" xml-lang="en-US" l10n="U" oldref="237">
 392 <item type="input">=NOMINAL_ADD(5.3543%;4)</item> returns 0.0525 or 5.25%.</paragraph>
 393 </section>
 394 <section id="dollarfr">
 395 <bookmark xml-lang="en-US" branch="index" id="bm_id3159087"><bookmark_value>DOLLARFR function</bookmark_value>
 396 <bookmark_value>converting;decimal fractions, into mixed decimal fractions</bookmark_value>
 397 </bookmark><comment>mw added one entry</comment>
 398 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_DOLLARFR" id="bm_id3146907" localize="false"/>
 399 <paragraph role="heading" id="hd_id3159087" xml-lang="en-US" level="2" oldref="208">DOLLARFR</paragraph>
 400 <paragraph role="paragraph" id="par_id3150593" xml-lang="en-US" l10n="U" oldref="209"><ahelp hid="HID_AAI_FUNC_DOLLARFR">Converts a quotation that has been given as a decimal number into a mixed decimal fraction.</ahelp></paragraph>
 401 <paragraph role="heading" id="hd_id3151106" xml-lang="en-US" level="3" l10n="U" oldref="210">Syntax</paragraph>
 402 <paragraph role="code" id="par_id3152959" xml-lang="en-US" l10n="U" oldref="211">DOLLARFR(DecimalDollar; Fraction)</paragraph>
 403 <paragraph role="paragraph" id="par_id3149558" xml-lang="en-US" l10n="U" oldref="212">
 404 <emph>DecimalDollar</emph> is a decimal number.</paragraph>
 405 <paragraph role="paragraph" id="par_id3153672" xml-lang="en-US" l10n="U" oldref="213">
 406 <emph>Fraction</emph> is a whole number that is used as the denominator of the decimal fraction.</paragraph>
 407 <paragraph role="heading" id="hd_id3156274" xml-lang="en-US" level="3" l10n="U" oldref="214">Example</paragraph>
 408 <paragraph role="paragraph" id="par_id3153795" xml-lang="en-US" l10n="U" oldref="215">
 409 <item type="input">=DOLLARFR(1.125;16)</item> converts into sixteenths. The result is 1.02 for 1 plus 2/16.</paragraph>
 410 <paragraph role="paragraph" id="par_id3150995" xml-lang="en-US" l10n="U" oldref="216">
 411 <item type="input">=DOLLARFR(1.125;8)</item> converts into eighths. The result is 1.1 for 1 plus 1/8.</paragraph>
 412 </section>
 413 <section id="dollarde">
 414 <bookmark xml-lang="en-US" branch="index" id="bm_id3154671"><bookmark_value>fractions; converting</bookmark_value>
 415 <bookmark_value>converting;decimal fractions, into decimal numbers</bookmark_value>
 416 <bookmark_value>DOLLARDE function</bookmark_value>
 417 </bookmark><comment>mw added one entry</comment>
 418 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_DOLLARDE" id="bm_id3154569" localize="false"/>
 419 <paragraph role="heading" id="hd_id3154671" xml-lang="en-US" level="2" oldref="199">DOLLARDE</paragraph>
 420 <paragraph role="paragraph" id="par_id3154418" xml-lang="en-US" l10n="U" oldref="200"><ahelp hid="HID_AAI_FUNC_DOLLARDE">Converts a quotation that has been given as a decimal fraction into a decimal number.</ahelp></paragraph>
 421 <paragraph role="heading" id="hd_id3146124" xml-lang="en-US" level="3" l10n="U" oldref="201">Syntax</paragraph>
 422 <paragraph role="code" id="par_id3150348" xml-lang="en-US" l10n="U" oldref="202">DOLLARDE(FractionalDollar; Fraction)</paragraph>
 423 <paragraph role="paragraph" id="par_id3154111" xml-lang="en-US" l10n="U" oldref="203">
 424 <emph>FractionalDollar</emph> is a number given as a decimal fraction.</paragraph>
 425 <paragraph role="paragraph" id="par_id3153695" xml-lang="en-US" l10n="U" oldref="204">
 426 <emph>Fraction</emph> is a whole number that is used as the denominator of the decimal fraction.</paragraph>
 427 <paragraph role="heading" id="hd_id3153884" xml-lang="en-US" level="3" l10n="U" oldref="205">Example</paragraph>
 428 <paragraph role="paragraph" id="par_id3150941" xml-lang="en-US" l10n="U" oldref="206">
 429 <item type="input">=DOLLARDE(1.02;16)</item> stands for 1 and 2/16. This returns 1.125.</paragraph>
 430 <paragraph role="paragraph" id="par_id3150830" xml-lang="en-US" l10n="U" oldref="207">
 431 <item type="input">=DOLLARDE(1.1;8)</item> stands for 1 and 1/8. This returns 1.125.</paragraph>
 432 </section>
 433 <section id="mirr">
 434 <bookmark xml-lang="en-US" branch="index" id="bm_id3148974"><bookmark_value>calculating;modified internal rates of return</bookmark_value>
 435 <bookmark_value>modified internal rates of return</bookmark_value>
 436 <bookmark_value>MIRR function</bookmark_value>
 437 <bookmark_value>internal rates of return;modified</bookmark_value>
 438 </bookmark><comment>mw added "internal rates of return;..."</comment>
 439 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_QIKV" id="bm_id3150670" localize="false"/>
 440 <paragraph role="heading" id="hd_id3148974" xml-lang="en-US" level="2" l10n="U" oldref="321">MIRR</paragraph>
 441 <paragraph role="paragraph" id="par_id3155497" xml-lang="en-US" l10n="U" oldref="322"><ahelp hid="HID_FUNC_QIKV">Calculates the modified internal rate of return of a series of investments.</ahelp></paragraph>
 442 <paragraph role="heading" id="hd_id3154354" xml-lang="en-US" level="3" l10n="U" oldref="323">Syntax</paragraph>
 443 <paragraph role="code" id="par_id3148399" xml-lang="en-US" l10n="U" oldref="324">MIRR(Values; Investment; ReinvestRate)</paragraph>
 444 <paragraph role="paragraph" id="par_id3155896" xml-lang="en-US" l10n="U" oldref="325">
 445 <emph>Values</emph> corresponds to the array or the cell reference for cells whose content corresponds to the payments.</paragraph>
 446 <paragraph role="paragraph" id="par_id3149998" xml-lang="en-US" l10n="U" oldref="326">
 447 <emph>Investment</emph> is the rate of interest of the investments (the negative values of the array)</paragraph>
 448 <paragraph role="paragraph" id="par_id3159408" xml-lang="en-US" l10n="U" oldref="327">
 449 <emph>ReinvestRate</emph>:the rate of interest of the reinvestment (the positive values of the array)</paragraph>
 450 <paragraph role="heading" id="hd_id3154714" xml-lang="en-US" level="3" l10n="U" oldref="328">Example</paragraph>
 451 <paragraph role="paragraph" id="par_id3147352" xml-lang="en-US" l10n="U" oldref="329">Assuming a cell content of A1 = <item type="input">-5</item>, A2 = <item type="input">10</item>, A3 = <item type="input">15</item>, and A4 = <item type="input">8</item>, and an investment value of 0.5 and a reinvestment value of 0.1, the result is 94.16%.</paragraph>
 452 </section>
 453 <section id="yield">
 454 <bookmark xml-lang="en-US" branch="index" id="bm_id3149323"><bookmark_value>YIELD function</bookmark_value>
 455 <bookmark_value>rates of return;securities</bookmark_value>
 456 <bookmark_value>yields, see also rates of return</bookmark_value>
 457 </bookmark><comment>mw added two entries</comment>
 458 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_YIELD" id="bm_id3152460" localize="false"/>
 459 <paragraph role="heading" id="hd_id3149323" xml-lang="en-US" level="2" oldref="129">YIELD</paragraph>
 460 <paragraph role="paragraph" id="par_id3150643" xml-lang="en-US" l10n="U" oldref="130"><ahelp hid="HID_AAI_FUNC_YIELD">Calculates the yield of a security.</ahelp></paragraph>
 461 <paragraph role="heading" id="hd_id3149344" xml-lang="en-US" level="3" l10n="U" oldref="131">Syntax</paragraph>
 462 <paragraph role="code" id="par_id3149744" xml-lang="en-US" l10n="U" oldref="132">YIELD(Settlement; Maturity; Rate; Price; Redemption; Frequency; Basis)</paragraph>
 463 <paragraph role="paragraph" id="par_id3154526" xml-lang="en-US" l10n="U" oldref="133">
 464 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 465 <paragraph role="paragraph" id="par_id3153266" xml-lang="en-US" l10n="U" oldref="134">
 466 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 467 <paragraph role="paragraph" id="par_id3151284" xml-lang="en-US" l10n="U" oldref="135">
 468 <emph>Rate</emph> is the annual rate of interest.</paragraph>
 469 <paragraph role="paragraph" id="par_id3147314" xml-lang="en-US" l10n="U" oldref="136">
 470 <emph>Price</emph> is the price (purchase price) of the security per 100 currency units of par value.</paragraph>
 471 <paragraph role="paragraph" id="par_id3145156" xml-lang="en-US" l10n="U" oldref="137">
 472 <emph>Redemption</emph> is the redemption value per 100 currency units of par value.</paragraph>
 473 <paragraph role="paragraph" id="par_id3159218" xml-lang="en-US" l10n="U" oldref="138">
 474 <emph>Frequency</emph> is the number of interest payments per year (1, 2 or 4).</paragraph>
 475 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 476 <paragraph role="heading" id="hd_id3147547" xml-lang="en-US" level="3" l10n="U" oldref="139">Example</paragraph>
 477 <paragraph role="paragraph" id="par_id3151214" xml-lang="en-US" l10n="CHG" oldref="140">A security is purchased on 1999-02-15. It matures on 2007-11-15. The rate of interest is 5.75%. The price is 95.04287 currency units per 100 units of par value, the redemption value is 100 units. Interest is paid half-yearly (frequency = 2) and the basis is 0. How high is the yield?</paragraph>
 478 <paragraph role="paragraph" id="par_id3154194" xml-lang="en-US" l10n="CHG" oldref="141">=YIELD("1999-02-15"; "2007-11-15"; 0.0575 ;95.04287; 100; 2; 0) returns 0.065 or 6.50 per cent.</paragraph>
 479 </section>
 480 <section id="yielddisc">
 481 <bookmark xml-lang="en-US" branch="index" id="bm_id3150100"><bookmark_value>YIELDDISC function</bookmark_value>
 482 <bookmark_value>rates of return;non-interest-bearing securities</bookmark_value>
 483 </bookmark><comment>mw added one entry</comment>
 484 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_YIELDDISC" id="bm_id3156206" localize="false"/>
 485 <paragraph role="heading" id="hd_id3150100" xml-lang="en-US" level="2" oldref="142">YIELDDISC</paragraph>
 486 <paragraph role="paragraph" id="par_id3150486" xml-lang="en-US" l10n="U" oldref="143"><ahelp hid="HID_AAI_FUNC_YIELDDISC">Calculates the annual yield of a non-interest-bearing security.</ahelp></paragraph>
 487 <paragraph role="heading" id="hd_id3149171" xml-lang="en-US" level="3" l10n="U" oldref="144">Syntax</paragraph>
 488 <paragraph role="code" id="par_id3159191" xml-lang="en-US" l10n="U" oldref="145">YIELDDISC(Settlement; Maturity; Price; Redemption; Basis)</paragraph>
 489 <paragraph role="paragraph" id="par_id3150237" xml-lang="en-US" l10n="U" oldref="146">
 490 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 491 <paragraph role="paragraph" id="par_id3146924" xml-lang="en-US" l10n="U" oldref="147">
 492 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 493 <paragraph role="paragraph" id="par_id3151201" xml-lang="en-US" l10n="U" oldref="148">
 494 <emph>Price</emph> is the price (purchase price) of the security per 100 currency units of par value.</paragraph>
 495 <paragraph role="paragraph" id="par_id3156049" xml-lang="en-US" l10n="U" oldref="149">
 496 <emph>Redemption</emph> is the redemption value per 100 currency units of par value.</paragraph>
 497 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 498 <paragraph role="heading" id="hd_id3154139" xml-lang="en-US" level="3" l10n="U" oldref="150">Example</paragraph>
 499 <paragraph role="paragraph" id="par_id3163815" xml-lang="en-US" l10n="CHG" oldref="151">A non-interest-bearing security is purchased on 1999-02-15. It matures on 1999-03-01. The price is 99.795 currency units per 100 units of par value, the redemption value is 100 units. The basis is 2. How high is the yield?</paragraph>
 500 <paragraph role="paragraph" id="par_id3155187" xml-lang="en-US" l10n="CHG" oldref="152">=YIELDDISC("1999-02-15"; "1999-03-01"; 99.795; 100; 2) returns 0.052823 or 5.2823 per cent.</paragraph>
 501 </section>
 502 <section id="yieldmat">
 503 <bookmark xml-lang="en-US" branch="index" id="bm_id3155140"><bookmark_value>YIELDMAT function</bookmark_value>
 504 <bookmark_value>rates of return;securities with interest paid on maturity</bookmark_value>
 505 </bookmark><comment>mw added one entry</comment>
 506 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_YIELDMAT" id="bm_id3156029" localize="false"/>
 507 <paragraph role="heading" id="hd_id3155140" xml-lang="en-US" level="2" oldref="153">YIELDMAT</paragraph>
 508 <paragraph role="paragraph" id="par_id3151332" xml-lang="en-US" l10n="U" oldref="154"><ahelp hid="HID_AAI_FUNC_YIELDMAT">Calculates the annual yield of a security, the interest of which is paid on the date of maturity.</ahelp></paragraph>
 509 <paragraph role="heading" id="hd_id3159100" xml-lang="en-US" level="3" l10n="U" oldref="155">Syntax</paragraph>
 510 <paragraph role="code" id="par_id3159113" xml-lang="en-US" l10n="U" oldref="156">YIELDMAT(Settlement; Maturity; Issue; Rate; Price; Basis)</paragraph>
 511 <paragraph role="paragraph" id="par_id3149309" xml-lang="en-US" l10n="U" oldref="157">
 512 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 513 <paragraph role="paragraph" id="par_id3151381" xml-lang="en-US" l10n="U" oldref="158">
 514 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 515 <paragraph role="paragraph" id="par_id3153302" xml-lang="en-US" l10n="U" oldref="159">
 516 <emph>Issue</emph> is the date of issue of the security.</paragraph>
 517 <paragraph role="paragraph" id="par_id3147140" xml-lang="en-US" l10n="U" oldref="160">
 518 <emph>Rate</emph> is the interest rate of the security on the issue date.</paragraph>
 519 <paragraph role="paragraph" id="par_id3151067" xml-lang="en-US" l10n="U" oldref="161">
 520 <emph>Price</emph> is the price (purchase price) of the security per 100 currency units of par value.</paragraph>
 521 <embed href="text/scalc/01/func_yearfrac.xhp#basis"/>
 522 <paragraph role="heading" id="hd_id3155342" xml-lang="en-US" level="3" l10n="U" oldref="162">Example</paragraph>
 523 <paragraph role="paragraph" id="par_id3163717" xml-lang="en-US" l10n="CHG" oldref="163">A security is purchased on 1999-03-15. It matures on 1999-11-03. The issue date was 1998-11-08. The rate of interest is 6.25%, the price is 100.0123 units. The basis is 0. How high is the yield?</paragraph>
 524 <paragraph role="paragraph" id="par_id3155311" xml-lang="en-US" l10n="CHG" oldref="164">=YIELDMAT("1999-03-15"; "1999-11-03"; "1998-11-08"; 0.0625; 100.0123; 0) returns 0.060954 or 6.0954 per cent.</paragraph>
 525 </section>
 526 <section id="pmt">
 527 <bookmark xml-lang="en-US" branch="index" id="bm_id3149577"><bookmark_value>calculating;annuities</bookmark_value>
 528 <bookmark_value>annuities</bookmark_value>
 529 <bookmark_value>PMT function</bookmark_value>
 530 </bookmark>
 531 <bookmark xml-lang="en-US" branch="hid/HID_FUNC_RMZ" id="bm_id3148895" localize="false"/>
 532 <paragraph role="heading" id="hd_id3149577" xml-lang="en-US" level="2" l10n="U" oldref="330">PMT</paragraph>
 533 <paragraph role="paragraph" id="par_id3148563" xml-lang="en-US" l10n="U" oldref="331"><ahelp hid="HID_FUNC_RMZ">Returns the periodic payment for an annuity with constant interest rates.</ahelp></paragraph>
 534 <paragraph role="heading" id="hd_id3145257" xml-lang="en-US" level="3" l10n="U" oldref="332">Syntax</paragraph>
 535 <paragraph role="code" id="par_id3147278" xml-lang="en-US" l10n="U" oldref="333">PMT(Rate; NPer; PV; FV; Type)</paragraph>
 536 <paragraph role="paragraph" id="par_id3147291" xml-lang="en-US" l10n="U" oldref="334">
 537 <emph>Rate</emph> is the periodic interest rate.</paragraph>
 538 <paragraph role="paragraph" id="par_id3148641" xml-lang="en-US" l10n="U" oldref="335">
 539 <emph>NPer</emph> is the number of periods in which annuity is paid.</paragraph>
 540 <paragraph role="paragraph" id="par_id3156360" xml-lang="en-US" l10n="U" oldref="336">
 541 <emph>PV</emph> is the present value (cash value) in a sequence of payments.</paragraph>
 542 <paragraph role="paragraph" id="par_id3154920" xml-lang="en-US" l10n="U" oldref="337">
 543 <emph>FV</emph> (optional) is the desired value (future value) to be reached at the end of the periodic payments.</paragraph>
 544 <paragraph role="paragraph" id="par_id3156434" xml-lang="en-US" l10n="U" oldref="338">
 545 <emph>Type</emph> (optional) is the due date for the periodic payments. Type=1 is payment at the beginning and Type=0 is payment at the end of each period.</paragraph>
 546 <paragraph role="paragraph" id="par_idN11645" xml-lang="en-US" l10n="NEW">
 547 <embedvar href="text/scalc/00/00000004.xhp#optional"/>
 548 </paragraph>
 549 <paragraph role="heading" id="hd_id3152358" xml-lang="en-US" level="3" l10n="U" oldref="339">Example</paragraph>
 550 <paragraph role="paragraph" id="par_id3154222" xml-lang="en-US" l10n="U" oldref="340">What are the periodic payments at a yearly interest rate of 1.99% if the payment time is 3 years and the cash value is 25,000 currency units. There are 36 months as 36 payment periods, and the interest rate per payment period is 1.99%/12.</paragraph>
 551 <paragraph role="paragraph" id="par_id3155943" xml-lang="en-US" l10n="U" oldref="341">
 552 <item type="input">=PMT(1.99%/12;36;25000)</item> = -715.96 currency units. The periodic monthly payment is therefore 715.96 currency units.</paragraph>
 553 </section>
 554 <section id="tbilleq">
 555 <bookmark xml-lang="en-US" branch="index" id="bm_id3155799"><bookmark_value>TBILLEQ function</bookmark_value>
 556 <bookmark_value>treasury bills;annual return</bookmark_value>
 557 <bookmark_value>annual return on treasury bills</bookmark_value>
 558 </bookmark><comment>mw changed "treasury bills;..." and aded one entry</comment>
 559 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_TBILLEQ" id="bm_id3147380" localize="false"/>
 560 <paragraph role="heading" id="hd_id3155799" xml-lang="en-US" level="2" oldref="58">TBILLEQ</paragraph>
 561 <paragraph role="paragraph" id="par_id3154403" xml-lang="en-US" l10n="U" oldref="59"><ahelp hid="HID_AAI_FUNC_TBILLEQ">Calculates the annual return on a treasury bill ().</ahelp> A treasury bill is purchased on the settlement date and sold at the full par value on the maturity date, that must fall within the same year. A discount is deducted from the purchase price.</paragraph>
 562 <paragraph role="heading" id="hd_id3155080" xml-lang="en-US" level="3" l10n="U" oldref="60">Syntax</paragraph>
 563 <paragraph role="code" id="par_id3150224" xml-lang="en-US" l10n="U" oldref="61">TBILLEQ(Settlement; Maturity; Discount)</paragraph>
 564 <paragraph role="paragraph" id="par_id3156190" xml-lang="en-US" l10n="U" oldref="62">
 565 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 566 <paragraph role="paragraph" id="par_id3153827" xml-lang="en-US" l10n="U" oldref="63">
 567 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 568 <paragraph role="paragraph" id="par_id3150310" xml-lang="en-US" l10n="U" oldref="64">
 569 <emph>Discount</emph> is the percentage discount on acquisition of the security.</paragraph>
 570 <paragraph role="heading" id="hd_id3150324" xml-lang="en-US" level="3" l10n="U" oldref="65">Example</paragraph>
 571 <paragraph role="paragraph" id="par_id3153173" xml-lang="en-US" l10n="U" oldref="66">Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9.14 per cent.</paragraph>
 572 <paragraph role="paragraph" id="par_id3153520" xml-lang="en-US" l10n="U" oldref="67">The return on the treasury bill corresponding to a security is worked out as follows:</paragraph>
 573 <paragraph role="paragraph" id="par_id3154382" xml-lang="en-US" l10n="CHG" oldref="68">=TBILLEQ("1999-03-31";"1999-06-01"; 0.0914) returns 0.094151 or 9.4151 per cent.</paragraph>
 574 </section>
 575 <section id="tbillprice">
 576 <bookmark xml-lang="en-US" branch="index" id="bm_id3151032"><bookmark_value>TBILLPRICE function</bookmark_value>
 577 <bookmark_value>treasury bills;prices</bookmark_value>
 578 <bookmark_value>prices;treasury bills</bookmark_value>
 579 </bookmark><comment>mw added two entries</comment>
 580 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_TBILLPRICE" id="bm_id3150576" localize="false"/>
 581 <paragraph role="heading" id="hd_id3151032" xml-lang="en-US" level="2" oldref="69">TBILLPRICE</paragraph>
 582 <paragraph role="paragraph" id="par_id3157887" xml-lang="en-US" l10n="U" oldref="70"><ahelp hid="HID_AAI_FUNC_TBILLPRICE">Calculates the price of a treasury bill per 100 currency units.</ahelp></paragraph>
 583 <paragraph role="heading" id="hd_id3156374" xml-lang="en-US" level="3" l10n="U" oldref="71">Syntax</paragraph>
 584 <paragraph role="code" id="par_id3150284" xml-lang="en-US" l10n="U" oldref="72">TBILLPRICE(Settlement; Maturity; Discount)</paragraph>
 585 <paragraph role="paragraph" id="par_id3154059" xml-lang="en-US" l10n="U" oldref="73">
 586 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 587 <paragraph role="paragraph" id="par_id3154073" xml-lang="en-US" l10n="U" oldref="74">
 588 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 589 <paragraph role="paragraph" id="par_id3145765" xml-lang="en-US" l10n="U" oldref="75">
 590 <emph>Discount</emph> is the percentage discount upon acquisition of the security.</paragraph>
 591 <paragraph role="heading" id="hd_id3153373" xml-lang="en-US" level="3" l10n="U" oldref="76">Example</paragraph>
 592 <paragraph role="paragraph" id="par_id3155542" xml-lang="en-US" l10n="U" oldref="77">Settlement date: March 31 1999, maturity date: June 1 1999, discount: 9 per cent.</paragraph>
 593 <paragraph role="paragraph" id="par_id3154578" xml-lang="en-US" l10n="U" oldref="78">The price of the treasury bill is worked out as follows:</paragraph>
 594 <paragraph role="paragraph" id="par_id3154592" xml-lang="en-US" l10n="CHG" oldref="79">=TBILLPRICE("1999-03-31";"1999-06-01"; 0.09) returns 98.45.</paragraph>
 595 </section>
 596 <section id="tbillyield">
 597 <bookmark xml-lang="en-US" branch="index" id="bm_id3152912"><bookmark_value>TBILLYIELD function</bookmark_value>
 598 <bookmark_value>treasury bills;rates of return</bookmark_value>
 599 <bookmark_value>rates of return of treasury bills</bookmark_value>
 600 </bookmark><comment>mw added two entries</comment>
 601 <bookmark xml-lang="en-US" branch="hid/HID_AAI_FUNC_TBILLYIELD" id="bm_id3151346" localize="false"/>
 602 <paragraph role="heading" id="hd_id3152912" xml-lang="en-US" level="2" oldref="80">TBILLYIELD</paragraph>
 603 <paragraph role="paragraph" id="par_id3145560" xml-lang="en-US" l10n="U" oldref="81"><ahelp hid="HID_AAI_FUNC_TBILLYIELD">Calculates the yield of a treasury bill.</ahelp></paragraph>
 604 <paragraph role="heading" id="hd_id3145578" xml-lang="en-US" level="3" l10n="U" oldref="82">Syntax</paragraph>
 605 <paragraph role="code" id="par_id3156077" xml-lang="en-US" l10n="U" oldref="83">TBILLYIELD(Settlement; Maturity; Price)</paragraph>
 606 <paragraph role="paragraph" id="par_id3156091" xml-lang="en-US" l10n="U" oldref="84">
 607 <emph>Settlement</emph> is the date of purchase of the security.</paragraph>
 608 <paragraph role="paragraph" id="par_id3157856" xml-lang="en-US" l10n="U" oldref="85">
 609 <emph>Maturity</emph> is the date on which the security matures (expires).</paragraph>
 610 <paragraph role="paragraph" id="par_id3149627" xml-lang="en-US" l10n="U" oldref="86">
 611 <emph>Price</emph> is the price (purchase price) of the treasury bill per 100 currency units of par value.</paragraph>
 612 <paragraph role="heading" id="hd_id3149642" xml-lang="en-US" level="3" l10n="U" oldref="87">Example</paragraph>
 613 <paragraph role="paragraph" id="par_id3145178" xml-lang="en-US" l10n="U" oldref="88">Settlement date: March 31 1999, maturity date: June 1 1999, price: 98.45 currency units.</paragraph>
 614 <paragraph role="paragraph" id="par_id3145193" xml-lang="en-US" l10n="U" oldref="89">The yield of the treasury bill is worked out as follows:</paragraph>
 615 <paragraph role="paragraph" id="par_id3148528" xml-lang="en-US" l10n="CHG" oldref="90">=TBILLYIELD("1999-03-31";"1999-06-01"; 98.45) returns 0.091417 or 9.1417 per cent.</paragraph>
 616 </section>
 617 </sort>
 618 <paragraph role="paragraph" id="par_id3148546" xml-lang="en-US" l10n="U" oldref="345"><link href="text/scalc/01/04060103.xhp" name="Back to Financial Functions Part One">Back to Financial Functions Part One</link></paragraph>
 619 <paragraph role="paragraph" id="par_id3146762" xml-lang="en-US" l10n="U" oldref="346"><link href="text/scalc/01/04060118.xhp" name="Forward to Financial Functions Part Three">Forward to Financial Functions Part Three</link></paragraph>
 620 <embed href="text/scalc/01/04060100.xhp#drking"/>
 621 </body>
 622 </helpdocument>