What would be the the mathematical equivalent of this excel formula? =PMT()

I need to create a JavaScript form that does the same calculation as this `=PMT()` function.

``````mortgage = 220000
rate= 4.75%
term = 30
``````

The example formula I have is `=PMT(4.75%/12,30*12,220000*-1)`

What would be the equation for this function? I tried to look up this function but it doesn't explain it very well.

The equation you want is: `P = (Pv*R) / [1 - (1 + R)^(-n)]`

where

• P = Monthly Payment
• Pv = Present Value (starting value of the loan)
• APR = Annual Percentage Rate
• R = Periodic Interest Rate = APR/number of interest periods per year
• n = Total number of interest periods (interest periods per year * number of years)

Using the variables above, the Excel =PMT() function is =PMT(R,n,Pv)

• rate (APR) = 4.75% (making R=4.75%/12 or 0.0475/12)
• mortgage (Pv) = 220000
• term (# of years) = 30 (n=30*12 with monthly payments)

The equation becomes:

```P = ((220000 * (0.0475/12)) / (1 - ((1 + (0.0475/12))^(-1 * 30 * 12))))
```

Or, with the original equation shown directly below it for comparison:

```P = ((220000 * (0.0475/12)) / (1 - ((1 + (0.0475/12))^(-1 * 30 * 12))))
P =  (  Pv   *     R      ) / (1 - ( 1 +       R    )^(     -n     )
```
• Which, if anyone is checking, equals \$1,147.62416. Commented Jun 27, 2017 at 6:58
• How can this formula be modified to include a fixed monthly increase in the loan, for example is the loan is a credit card and the user spends \$50 per month on the card? Commented Jan 4, 2022 at 10:36