Suppose you owe 75000 on a student loan The annual interest

Suppose you owe $75,000 on a student loan. The annual interest rate on the loan is 7.5%, the duration of the loan is 10 years, and you will make monthly payments on the loan. How much will you repay each month?

Solution

Present value = Monthly payment x PVIFA (r%, N months)

Monthly interest rate = 7.5% / 12 = 0.63%

Number of months = 10 x 12 = 120

PVIFA (r%, N) = [1 - (1 + r) ^{- N}] / r

PVIFA (0.63%, 120) = [1 - (1 + 0.0063) ^{- 120}] / 0.0063 = [1 - (1.0063)^{- 120}] / 0.0063 = [1 - 0.4707] / 0.0063

= 84.0229

So,

75,000 = A x 84.0229 [A: Monthly payment]

A = $892.61