7. Find the monthly payments on a $100,000 30 year mortgage if the annual interest rate is 8.5% compounded monthly.

What would the monthly payments be for a 15 year mortgage at the same interest rates?

The monthly payment formula is

Then the issue becomes, how does one punch that into the calculator. The reader shold verify that

R = Pr/m/(1 - (1 + r/m)-mt)

will work, where

P = 100,000

r = .085

m = 12

t = 30

R = 100,000x.085/12/(1 - (1 + .085/12)^(-12x30))

= $768.91

rounded to the nearest cent.

For the 15 year mortgage, use the same formula except use a 15 for t.

R = 100,000x.085/12/(1 - (1 + .085/12)^(-12x15))

= 984.74

rounded to the nearest cent.

With mortgage payments you really want to round up to the nearest cent. In the case of the 30 year mortgage that would give you $768.92 but it would give you the same answer as above for the 15 year mortgage.

In this case, the decimal representation of the periodic interest rate does not terminate. You will get more accuracy with fewer punches by typing in the formula as it is above than by typing in a rounded off approximation for the periodic interest rate.