# Mathematics of Finance

Richard borrowed 170000 dollars from his bank to help finance the purchase of a house. The bank charges interest a rate of 8.9 percent per year compounded monthly. Richard has agreed to repay the loan in equal monthly installments over 35 years.

a) How much should each payment be if the loan is to be amortized at the end of the term?

b) How much, in total, will Richard spend on interest charges?

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1. i = .089/12 = .007416666.. (I used my calculator's memory to store that)
n = 35x12 = 420

Let the monthly payment be P
using the standard formula for the Present Value of an annuity,

170000 = P( 1 - 1.00741666..^-240 )/.00741666..
P = \$1320.09 -----> a)

b)
total paid = 120x1320.09 = \$554,437.80
so it looks like the total interest paid was \$384,437.80

(unfortunately, that is how mortgages over a long period of time work)

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posted by Reiny

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