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

Question

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.

Solution

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)

So, for your example where:

• 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     )

Comments

[Admin]

See also: quora.com/…

[Admin]

See also amortization calculator in Wikipedia.

[Admin]

Which, if anyone is checking, equals $1,147.62416.

[Admin]

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?