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I am trying to code the equivalent to the EXCEL PMT function.
in JavaScript, the formula looks like this:
function PMT (ir, np, pv, fv ) {
/*
ir - interest rate per month
np - number of periods (months)
pv - present value
fv - future value (residual value)
*/
pmt = ( ir * ( pv * Math.pow ( (ir+1), np ) + fv ) ) / ( ( ir + 1 ) * ( Math.pow ( (ir+1), np) -1 ) );
return pmt;
}
This is great for PMT calcs where Type =1 (i.e. payments occur at the start of the period)
However, I'm trying to code for a Type 0 scenario (i.e. payments occur at the end of the period)).
Any math wizards out there who can tell me how to modify my formula?
I am trying to code the equivalent to the EXCEL PMT function.
in JavaScript, the formula looks like this:
function PMT (ir, np, pv, fv ) {
/*
ir - interest rate per month
np - number of periods (months)
pv - present value
fv - future value (residual value)
*/
pmt = ( ir * ( pv * Math.pow ( (ir+1), np ) + fv ) ) / ( ( ir + 1 ) * ( Math.pow ( (ir+1), np) -1 ) );
return pmt;
}
This is great for PMT calcs where Type =1 (i.e. payments occur at the start of the period)
However, I'm trying to code for a Type 0 scenario (i.e. payments occur at the end of the period)).
Any math wizards out there who can tell me how to modify my formula?
Share Improve this question edited Oct 23, 2019 at 7:50 Brian Tompsett - 汤莱恩 5,89372 gold badges61 silver badges133 bronze badges asked Mar 18, 2011 at 14:37 dps123dps123 1,0736 gold badges19 silver badges26 bronze badges 1- Before you write your formulas, can you actually describe how they work? If you can't, better get over to Wikipedia and start reading ;) – Blender Commented Mar 18, 2011 at 14:43
4 Answers
Reset to default 4@dps123: When I recently had to work with some financial equations to convert functions from an Excel workbook, I came across the EGM Mathematical Finance class, which tries to mimic Excel functions. It might be worth having a look at, if only to see how the functions look/were made to work like Excel's.
Example usage:
<?php
/**
* Case use of financial class.
*
* @version $Id: financial_example.php,v 1.0.5 2004-06-23 09:03:56-05 egarcia Exp $
* @author Enrique Garcia M. <[email protected]>
* @copyright (c) 2002-2004 EGM :: Ingenieria sin fronteras
* @since Saturday, November 30, 2002
**/
/***************************************************************************
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
***************************************************************************/
include('financial_class.php');
echo '<pre>';
echo 'FV: ' . $f->FV(1.1, 1/360, 0, -100) . "\n";
echo 'PV: ' . $f->PV(1.1, 1/360, 0, -100.206306226) . "\n";
echo 'PMT: ' . $f->PMT(1.1, 1/360, -100) . "\n";
echo 'PMT: ' . $f->PMT(1.1, 1/360, 0, -100.206306226) . "\n";
echo 'NPER: ' . $f->NPER(1.1, 53428.7980679, -100) . "\n";
echo 'NPER: ' . $f->NPER(1.1, 0, -100, -100.206306226) . "\n";
echo 'FV: ' . $f->FV(0.1, 1/360, 0, -100) . "\n";
echo 'PV: ' . $f->PV(0.1, 1/360, 0, -100.026478555) . "\n";
echo 'PMT: ' . $f->PMT(0.1, 1/360, -100) . "\n";
echo 'PMT: ' . $f->PMT(0.1, 1/360, 0, -100.026478555) . "\n";
echo 'NPER: ' . $f->NPER(1.1, 37776.4114948, -100) . "\n";
echo 'NPER: ' . $f->NPER(1.1, 0, -100, -100.026478555) . "\n";
echo 'EFFECT: ' . $f->EFFECT(0.0525, 4) . "\n";
echo 'NOMINAL: ' . $f->NOMINAL(0.053543, 4) . "\n";
echo 'NPV: ' . $f->NPV(0.1, array(-10000,3000,4200,6800)) . "\n";
echo 'XNPV: ' . $f->XNPV(0.09, array(-10000,2750,4250,3250,2750), array(
mktime(0,0,0,1,1,2008),
mktime(0,0,0,3,1,2008),
mktime(0,0,0,10,30,2008),
mktime(0,0,0,2,15,2009),
mktime(0,0,0,4,1,2009),
)) . "\n";
echo 'XIRR: ' . $f->XIRR(array(-10000,2750,4250,3250,2750), array(
mktime(0,0,0,1,1,2008),
mktime(0,0,0,3,1,2008),
mktime(0,0,0,10,30,2008),
mktime(0,0,0,2,15,2009),
mktime(0,0,0,4,1,2009),
), 0.1) . "\n";
echo 'IRR: ' . $f->IRR(array(-70000,12000,15000,18000,21000)) . "\n";
echo 'DISC: ' . $f->DISC(
mktime(0,0,0,1,25,2007),
mktime(0,0,0,6,15,2007),
97.975,
100,
0) . "\n";
echo 'DISC: ' . $f->DISC(
mktime(0,0,0,1,25,2007),
mktime(0,0,0,6,15,2009),
97.975,
100,
1) . "\n";
echo 'DISC: ' . $f->DISC(
mktime(0,0,0,1,25,2007),
mktime(0,0,0,6,15,2007),
97.975,
100,
2) . "\n";
echo 'DISC: ' . $f->DISC(
mktime(0,0,0,1,25,2007),
mktime(0,0,0,6,15,2007),
97.975,
100,
3) . "\n";
echo 'DISC: ' . $f->DISC(
mktime(0,0,0,1,25,2007),
mktime(0,0,0,6,15,2007),
97.975,
100,
4) . "\n";
echo 'INTRATE: ' . $f->INTRATE(
mktime(0,0,0,2,15,2008),
mktime(0,0,0,5,15,2008),
1000000,
1014420,
2) . "\n";
echo 'IPMT: ' . $f->IPMT(0.1/12, 3, 3, 8000) . "\n";
echo 'IPMT: ' . $f->IPMT(0.1, 3, 3, 8000) . "\n";
echo 'RECEIVED: ' . $f->RECEIVED(
mktime(0,0,0,2,15,2008),
mktime(0,0,0,5,15,2008),
1000000,
0.0575,
2) . "\n";
echo 'DOLLARDE: ' . $f->DOLLARDE(1.02, 16) . "\n";
echo 'DOLLARDE: ' . $f->DOLLARDE(1.1, 32) . "\n";
echo 'DOLLARFR: ' . $f->DOLLARFR(1.125, 16) . "\n";
echo 'DOLLARFR: ' . $f->DOLLARFR(1.125, 32) . "\n";
echo 'FVSCHEDULE: ' . $f->FVSCHEDULE(1, array(0.09,0.11,0.1)) . "\n";
echo 'PPMT: ' . $f->PPMT(0.1/12, 1, 2*12, 2000) . "\n";
echo 'PPMT: ' . $f->PPMT(0.08, 10, 10, 200000) . "\n";
echo 'RATE: ' . $f->RATE(4*12,-200, 8000) . "\n";
echo 'RATE: ' . $f->RATE(4*12,-200, 8000)*12 . "\n";
echo 'SYD: ' . $f->SYD(30000, 7500, 10, 10) . "\n";
echo 'SLN: ' . $f->SLN(30000, 7500, 10) . "\n";
echo 'DDB: ' . $f->DDB(1000000, 100000, 10, 4) . "\n";
echo 'DELTA: ' . $f->DELTA(5, 4) . "\n";
echo 'DELTA: ' . $f->DELTA(5, 5) . "\n";
echo 'PRICEDISC: ' . $f->PRICEDISC(mktime(0,0,0,2,16,2008), mktime(0,0,0,3,1,2008), 0.0525, 100, 2) . "\n";
echo 'YIELDDISC: ' . $f->YIELDDISC(mktime(0,0,0,2,16,2008), mktime(0,0,0,3,1,2008), 99.795, 100, 2) . "\n";
echo 'COUPNUM: ' . $f->COUPNUM(mktime(0,0,0,1,25,2007), mktime(0,0,0,11,15,2008), 2, 1) . "\n";
echo 'COUPDAYBS: ' . $f->COUPDAYBS(mktime(0,0,0,1,25,2007), mktime(0,0,0,11,17,2008), 1, 1) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10*365,0,1) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10*12,0,1) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10,0,1) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10*12,6,18) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10*12,6,18,1.5) . "\n";
echo 'VDB: ' . $f->VDB(2400,300,10,0,0.875,1.5) . "\n";
echo 'MIRR: ' . $f->MIRR(array(-120000,39000,30000,21000,37000,46000), 0.1, 0.12) . "\n";
echo 'MIRR: ' . $f->MIRR(array(-120000,39000,30000,21000), 0.1, 0.12) . "\n";
echo 'MIRR: ' . $f->MIRR(array(-120000,39000,30000,21000,37000,46000), 0.1, 0.14) . "\n";
echo '</pre>';
?>
@dps
You would need to amend the denominator where the interest factor is changed to (ir * type + 1)
When it is an annuity due meaning start of period payments the value of 1 for Type will insure the interest factor (ir + 1) and when it is an ordinary annuity meaning end of period payments the value of 0 for Type will reduce the factor to 1.
pmt = ( ir * ( pv * Math.pow ( (ir+1), np ) + fv ) ) / ( ( ir * type + 1 ) * ( Math.pow ( (ir+1), np) -1 ) );
The equation you presented is actually how MS Excel putes 5 Time Value of Money functions namely FV, PV, PMT, NPER and RATE. The first three are easily calculated by rearranging the equation and solve for FV, PV or PMT. For NPER and RATE other methods are needed, some use a binary search algorithm to find RATE yet a better and elegant solution to find RATE is to be had with Newton Raphson method.
Below is the code in java:
double pmt = ((pv - fv) * ir / (1 - Math.pow((1 + ir), -np)));
I am not a math wiz, but a simple google search turned this thread up:
http://www.excelforum./excel-general/370948-pmt-function-does-anyone-know-the-formula.html
Here he has the following formula for type=0:
pmt = ((pv - fv) * ir / (1 - (1 + ir) ^ -(np)));
Maybe this will work for you :)
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