Equal Payment Loans

Equal payment loans are the most common type of loan calculated, and are usually the main focus of a lending institution. The four basic variables involved in an equal payment loan are: amount, rate, term and payment.

Most of the time, a user will want to specify the amount, rate and term, and then have the SCE compute the resulting payment. However, there are times when a specific payment is desired, and the amount or term must then be computed. The SCE supports these rollback calculations, and each is documented in this chapter.

Compute Payment

Most equal payment loan calculations are requested with the loan's proceeds, interest rate, and term known. The SCE then computes the regular payment that best amortizes the loan's ending balance to zero in accordance with the accrual method and options included in the loan request.

Sample Request

The following is a sample SCEX request for an equal payment loan calculation where the interest rate, proceeds, and term are specified and the regular payment is computed.

<inEQUAL_PMT Account="1" DataDirPath="C:\SCEX\" AccrualCode="32" PPY="monthly">
  <LoanDate>2024-10-18</LoanDate>
  <PmtDate>2024-11-18</PmtDate>
  <IntRate>10.123</IntRate>
  <Proceeds>10000.00</Proceeds>
  <TotalDown>2500.00</TotalDown>
  <Term>12</Term>
  <Fee Name="Fee1" CalcType="Dollar"
    Entry="25.00" MaxValue="25.00"
    AddToPrin="true" AddToFinChg="false" />
</inEQUAL_PMT>

Sample Response

The following is the XML response associated with the request above, at the time this documentation was being written (2024-10):

<?xml version="1.0" standalone="no" ?>
<!DOCTYPE outEQUAL_PMT SYSTEM "outEQUAL_PMT.dtd">
<outEQUAL_PMT>
   <Results>
      <Description>Successful Calculation</Description>
      <Payment>881.92</Payment>
   </Results>
   <FedBox>
      <AmtFin>10025.00</AmtFin>
      <FinChg>558.04</FinChg>
      <TotPmts>10583.04</TotPmts>
      <TotalSalePrice>13083.04</TotalSalePrice>
      <RegZAPR Type="Actuarial">10.121</RegZAPR>
   </FedBox>
   <Moneys>
      <Principal>10025.00</Principal>
      <Interest>558.04</Interest>
      <FinFees>25.00</FinFees>
      <Protection Category="None" PerPmt="0.00" PerDay="0.00">0.00</Protection>
      <Fee Name="Fee1">25.00</Fee>
   </Moneys>
   <Accrual>
      <Method>Actual/365 US Rule</Method>
      <Days1Pmt DayCount="Actual">31</Days1Pmt>
      <Maturity>2025-10-18</Maturity>
   </Accrual>
   <PmtStream Term="12" Pmt="881.92" Rate="10.123" Begin="2024-11-18"/>
   <AmTable>
      <GrandTotals PmtTot="10583.04" IntTot="558.05" PrinTot="10024.99"/>
      <SubTotals Year="2024" Start="1" Events="2" PmtSub="1763.84" IntSub="162.98" PrinSub="1600.86"/>
      <SubTotals Year="2025" Start="3" Events="10" PmtSub="8819.20" IntSub="395.07" PrinSub="8424.13"/>
      <AmLine Idx="1" Date="2024-11-18" BegBal="10025.00" Pmt="881.92" Int="86.19" Prin="795.73" EndBal="9229.27"/>
      <AmLine Idx="2" Date="2024-12-18" BegBal="9229.27" Pmt="881.92" Int="76.79" Prin="805.13" EndBal="8424.14"/>
      <AmLine Idx="3" Date="2025-01-18" BegBal="8424.14" Pmt="881.92" Int="72.43" Prin="809.49" EndBal="7614.65"/>
      <AmLine Idx="4" Date="2025-02-18" BegBal="7614.65" Pmt="881.92" Int="65.47" Prin="816.45" EndBal="6798.20"/>
      <AmLine Idx="5" Date="2025-03-18" BegBal="6798.20" Pmt="881.92" Int="52.79" Prin="829.13" EndBal="5969.07"/>
      <AmLine Idx="6" Date="2025-04-18" BegBal="5969.07" Pmt="881.92" Int="51.32" Prin="830.60" EndBal="5138.47"/>
      <AmLine Idx="7" Date="2025-05-18" BegBal="5138.47" Pmt="881.92" Int="42.75" Prin="839.17" EndBal="4299.30"/>
      <AmLine Idx="8" Date="2025-06-18" BegBal="4299.30" Pmt="881.92" Int="36.96" Prin="844.96" EndBal="3454.34"/>
      <AmLine Idx="9" Date="2025-07-18" BegBal="3454.34" Pmt="881.92" Int="28.74" Prin="853.18" EndBal="2601.16"/>
      <AmLine Idx="10" Date="2025-08-18" BegBal="2601.16" Pmt="881.92" Int="22.36" Prin="859.56" EndBal="1741.60"/>
      <AmLine Idx="11" Date="2025-09-18" BegBal="1741.60" Pmt="881.92" Int="14.97" Prin="866.95" EndBal="874.65"/>
      <AmLine Idx="12" Date="2025-10-18" BegBal="874.65" Pmt="881.92" Int="7.28" Prin="874.64" EndBal="0.01"/>
   </AmTable>
</outEQUAL_PMT>

Roll to Amount

Instead of specifying the interest rate, amount, and term and then computing a payment, sometimes it is helpful for the borrower to be able to specify a desired payment, rate and term and then see what amount the borrower can afford to borrower. Sherman and Associates calls this type of calculation a Roll to Amount.

Sample Request

The following is a sample SCEX request for an equal payment loan calculation where the loan amount (i.e. proceeds) is computed.

<inEQUAL_PROCEEDS Account="2" AccrualCode="330" DataDirPath="C:\SCEX\" PPY="monthly">
  <LoanDate>2024-10-18</LoanDate>
  <PmtDate>2024-11-18</PmtDate>
  <IntRate>10.123</IntRate>
  <Payment>300.00</Payment>
  <Term>12</Term>
  <Fee Entry="25.00" MaxValue="25.00" CalcType="Dollar" 
    AddToPrin="true" AddToFinChg="false" />
</inEQUAL_PROCEEDS>

Sample Response

The following is the XML response associated with the roll to amount request above, at the time this documentation was being written (2024-10):

<?xml version="1.0" standalone="no" ?>
<!DOCTYPE outEQUAL_PROCEEDS SYSTEM "outEQUAL_PROCEEDS.dtd">
<outEQUAL_PROCEEDS>
   <Results>
      <Description>Successful Calculation</Description>
      <Proceeds>3385.34</Proceeds>
      <Payment>300.00</Payment>
      <Final>300.00</Final>
   </Results>
   <FedBox>
      <AmtFin>3410.34</AmtFin>
      <FinChg>189.66</FinChg>
      <TotPmts>3600.00</TotPmts>
      <RegZAPR Type="Actuarial">10.112</RegZAPR>
   </FedBox>
   <Moneys>
      <Principal>3410.34</Principal>
      <Interest>189.66</Interest>
      <FinFees>25.00</FinFees>
      <Protection Category="None" PerPmt="0.00" PerDay="0.00">0.00</Protection>
      <Fee>25.00</Fee>
   </Moneys>
   <Accrual>
      <Method>Actual/Actual US Rule</Method>
      <Days1Pmt DayCount="Actual">31</Days1Pmt>
      <Maturity>2025-10-18</Maturity>
   </Accrual>
   <PmtStream Term="12" Pmt="300.00" Rate="10.123" Begin="2024-11-18"/>
   <AmTable>
      <GrandTotals PmtTot="3600.00" IntTot="189.66" PrinTot="3410.34"/>
      <SubTotals Year="2024" Start="1" Events="2" PmtSub="600.00" IntSub="55.29" PrinSub="544.71"/>
      <SubTotals Year="2025" Start="3" Events="10" PmtSub="3000.00" IntSub="134.37" PrinSub="2865.63"/>
      <AmLine Idx="1" Date="2024-11-18" BegBal="3410.34" Pmt="300.00" Int="29.24" Prin="270.76" EndBal="3139.58"/>
      <AmLine Idx="2" Date="2024-12-18" BegBal="3139.58" Pmt="300.00" Int="26.05" Prin="273.95" EndBal="2865.63"/>
      <AmLine Idx="3" Date="2025-01-18" BegBal="2865.63" Pmt="300.00" Int="24.61" Prin="275.39" EndBal="2590.24"/>
      <AmLine Idx="4" Date="2025-02-18" BegBal="2590.24" Pmt="300.00" Int="22.27" Prin="277.73" EndBal="2312.51"/>
      <AmLine Idx="5" Date="2025-03-18" BegBal="2312.51" Pmt="300.00" Int="17.96" Prin="282.04" EndBal="2030.47"/>
      <AmLine Idx="6" Date="2025-04-18" BegBal="2030.47" Pmt="300.00" Int="17.46" Prin="282.54" EndBal="1747.93"/>
      <AmLine Idx="7" Date="2025-05-18" BegBal="1747.93" Pmt="300.00" Int="14.54" Prin="285.46" EndBal="1462.47"/>
      <AmLine Idx="8" Date="2025-06-18" BegBal="1462.47" Pmt="300.00" Int="12.57" Prin="287.43" EndBal="1175.04"/>
      <AmLine Idx="9" Date="2025-07-18" BegBal="1175.04" Pmt="300.00" Int="9.78" Prin="290.22" EndBal="884.82"/>
      <AmLine Idx="10" Date="2025-08-18" BegBal="884.82" Pmt="300.00" Int="7.61" Prin="292.39" EndBal="592.43"/>
      <AmLine Idx="11" Date="2025-09-18" BegBal="592.43" Pmt="300.00" Int="5.09" Prin="294.91" EndBal="297.52"/>
      <AmLine Idx="12" Date="2025-10-18" BegBal="297.52" Pmt="300.00" Int="2.48" Prin="297.52" EndBal="0.00"/>
   </AmTable>
</outEQUAL_PROCEEDS>

Roll to Term

The roll to term calculation computes a loan amount given an interest rate, proceeds, and desired payment.

Note that the term returned will be the minimum term such that the computed payment is less than or equal to the desired payment. Since the number of payments in a loan is an integer, it is most often the case that the resulting payment will not exactly match the desired payment. However, it is guaranteed to be less than or equal to the desired payment.

Sample Request

The following is a sample SCEX request for an equal payment loan calculation where the loan term is computed.

<inEQUAL_TERM Account="1" AccrualCode="202"
 DataDirPath="C:\SCEX\" PPY="monthly">
 <LoanDate>2024-10-18</LoanDate>
 <PmtDate>2024-11-18</PmtDate>
 <IntRate>10.123</IntRate>
 <Proceeds>7500.00</Proceeds>
 <Payment>400.00</Payment>
 <Fee Entry="25.00" MaxValue="25.00" CalcType="Dollar"
   AddToPrin="true" AddToFinChg="false" />
</inEQUAL_TERM>

Sample Response

The following is the XML response associated with the roll to term request above, at the time this documentation was being written (2024-10):

<?xml version="1.0" standalone="no" ?>
<!DOCTYPE outEQUAL_TERM SYSTEM "outEQUAL_TERM.dtd">
<outEQUAL_TERM>
   <Results>
      <Description>Successful Calculation</Description>
      <Term>21</Term>
      <Payment>392.58</Payment>
   </Results>
   <FedBox>
      <AmtFin>7525.00</AmtFin>
      <FinChg>719.18</FinChg>
      <TotPmts>8244.18</TotPmts>
      <RegZAPR Type="Actuarial">10.142</RegZAPR>
   </FedBox>
   <Moneys>
      <Principal>7525.00</Principal>
      <Interest>719.18</Interest>
      <FinFees>25.00</FinFees>
      <Protection Category="None" PerPmt="0.00" PerDay="0.00">0.00</Protection>
      <Fee>25.00</Fee>
   </Moneys>
   <Accrual>
      <Method>Unit Period 365 Simple</Method>
      <Days1Pmt DayCount="Actual">31</Days1Pmt>
      <Maturity>2026-07-18</Maturity>
   </Accrual>
   <PmtStream Term="21" Pmt="392.58" Rate="10.123" Begin="2024-11-18"/>
   <AmTable>
      <GrandTotals PmtTot="8244.18" IntTot="719.13" PrinTot="7525.05"/>
      <SubTotals Year="2024" Start="1" Events="2" PmtSub="785.16" IntSub="125.41" PrinSub="659.75"/>
      <SubTotals Year="2025" Start="3" Events="12" PmtSub="4710.96" IntSub="503.29" PrinSub="4207.67"/>
      <SubTotals Year="2026" Start="15" Events="7" PmtSub="2748.06" IntSub="90.43" PrinSub="2657.63"/>
      <AmLine Idx="1" Date="2024-11-18" BegBal="7525.00" Pmt="392.58" Int="64.70" Prin="327.88" EndBal="7197.12"/>
      <AmLine Idx="2" Date="2024-12-18" BegBal="7197.12" Pmt="392.58" Int="60.71" Prin="331.87" EndBal="6865.25"/>
      <AmLine Idx="3" Date="2025-01-18" BegBal="6865.25" Pmt="392.58" Int="57.91" Prin="334.67" EndBal="6530.58"/>
      <AmLine Idx="4" Date="2025-02-18" BegBal="6530.58" Pmt="392.58" Int="55.09" Prin="337.49" EndBal="6193.09"/>
      <AmLine Idx="5" Date="2025-03-18" BegBal="6193.09" Pmt="392.58" Int="52.24" Prin="340.34" EndBal="5852.75"/>
      <AmLine Idx="6" Date="2025-04-18" BegBal="5852.75" Pmt="392.58" Int="49.37" Prin="343.21" EndBal="5509.54"/>
      <AmLine Idx="7" Date="2025-05-18" BegBal="5509.54" Pmt="392.58" Int="46.48" Prin="346.10" EndBal="5163.44"/>
      <AmLine Idx="8" Date="2025-06-18" BegBal="5163.44" Pmt="392.58" Int="43.56" Prin="349.02" EndBal="4814.42"/>
      <AmLine Idx="9" Date="2025-07-18" BegBal="4814.42" Pmt="392.58" Int="40.61" Prin="351.97" EndBal="4462.45"/>
      <AmLine Idx="10" Date="2025-08-18" BegBal="4462.45" Pmt="392.58" Int="37.64" Prin="354.94" EndBal="4107.51"/>
      <AmLine Idx="11" Date="2025-09-18" BegBal="4107.51" Pmt="392.58" Int="34.65" Prin="357.93" EndBal="3749.58"/>
      <AmLine Idx="12" Date="2025-10-18" BegBal="3749.58" Pmt="392.58" Int="31.63" Prin="360.95" EndBal="3388.63"/>
      <AmLine Idx="13" Date="2025-11-18" BegBal="3388.63" Pmt="392.58" Int="28.59" Prin="363.99" EndBal="3024.64"/>
      <AmLine Idx="14" Date="2025-12-18" BegBal="3024.64" Pmt="392.58" Int="25.52" Prin="367.06" EndBal="2657.58"/>
      <AmLine Idx="15" Date="2026-01-18" BegBal="2657.58" Pmt="392.58" Int="22.42" Prin="370.16" EndBal="2287.42"/>
      <AmLine Idx="16" Date="2026-02-18" BegBal="2287.42" Pmt="392.58" Int="19.30" Prin="373.28" EndBal="1914.14"/>
      <AmLine Idx="17" Date="2026-03-18" BegBal="1914.14" Pmt="392.58" Int="16.15" Prin="376.43" EndBal="1537.71"/>
      <AmLine Idx="18" Date="2026-04-18" BegBal="1537.71" Pmt="392.58" Int="12.97" Prin="379.61" EndBal="1158.10"/>
      <AmLine Idx="19" Date="2026-05-18" BegBal="1158.10" Pmt="392.58" Int="9.77" Prin="382.81" EndBal="775.29"/>
      <AmLine Idx="20" Date="2026-06-18" BegBal="775.29" Pmt="392.58" Int="6.54" Prin="386.04" EndBal="389.25"/>
      <AmLine Idx="21" Date="2026-07-18" BegBal="389.25" Pmt="392.58" Int="3.28" Prin="389.30" EndBal="-0.05"/>
   </AmTable>
</outEQUAL_TERM>