How to calculate the monthly payment needed to reach a certain amount in savings account?

Question

I am trying to use Javascript to get the monthly payment needed to reach a certain amount of money in a savings account given the annual interest rate, savings starting amount, final amount, and the amount of time to let it grow. Here is an example:

PV=1000
FV=10000
Nper = 5 * 12 = 60
Rate = 1% /12 = 0.0083%

Somehow the answer is $145.51 but every formula I try gives a different result. On excel it is used like this to get this answer: PMT(0.083%,60,1000,-10000), and I tried the following:

var pv = 1000;
var fv = -10000;
var i = 0.01 / 12;
var n = 60;

function payment() {
  return (pv - fv) * (i) / (1 - (Math.pow(1 + i, -n)));
}

This did not give the desired answer. This gives me 188.03 and not 145.51. Any idea why?? Is this not the correct equation? Thanks!

Answer 1

Here is the correct equation for PMT. I've added a quick integration for verification. Source : https://gist.github.com/maarten00/23400873d51bf2ec4eeb

const pv = 1000;
const fv = -10000;
const i = 0.01 / 12;
const n = 60;

function pmt(rate_per_period, number_of_payments, present_value, future_value, type){
    future_value = typeof future_value !== 'undefined' ? future_value : 0;
    type = typeof type !== 'undefined' ? type : 0;

    if(rate_per_period != 0.0){
        // Interest rate exists
        var q = Math.pow(1 + rate_per_period, number_of_payments);
        return -(rate_per_period * (future_value + (q * present_value))) / ((-1 + q) * (1 + rate_per_period * (type)));

    } else if(number_of_payments != 0.0){
        // No interest rate, but number of payments exists
        return -(future_value + present_value) / number_of_payments;
    }

    return 0;
}

document.getElementById("showPayment").innerHTML = pmt(i, n, pv, fv);

<div class="showPayment" id="showPayment">

</div>