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

Solution 1:

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     )