Question

Suppose that you have just graduated with $30,000 in student loan debt, at 9% annual interest, compounded monthly. You must make a payment at the end of each month, and willbe finished paying off the loan at the end of 10 years.a. How much is each payment?

b. How much money, in total, will you end up paying by the time you have paid off the loan?
c. How much of what you will end up paying is interest?
d. [Just to think about, not to hand in: How painful is the answer to part c of this question?]

Answer 1

Explanation:

Principal amount = 30,000

I = 9% is compounded monthly ⇒ 0.09/12 = 0.0075

n= 10 years ⇒ 10* 12 = 120 periods

Formula for decreasing annuity payments is R =[ I/[1 - (1+I)^(-n)]] * P

R = 0.0075/[1 - 1.0075^(-120)] * 30,000 = $380, amount of each payment

Total amount paid is = 380*12*10 = 45600

Interest paid = Total amount - loan amount = 45600 - 30000 = 15600