You recently graduated and borrowed $10,000 from you parents. Your parents want you to be responsible and have asked that you repay them $100 per month payable at the end of each month. They also require a 6% compounded monthly interest charge. How many years before you will have this loan paid off?

Question

Quizplus · Accepted Answer

We can use the formula for the future value of an annuity with compound interest:

FV = PMT × [(1 + r)n - 1]/r

where:
PMT = monthly payment = $100
r = monthly interest rate = 6%/12 = 0.5%
n = number of months

We need to solve for n:

$10,000 = $100 × [(1 + 0.005)n - 1]/0.005

Multiplying both sides by 0.005 and simplifying:

50n = log(101) - log(100)

50n = log(1.01)

n = log(1.01)/50

n ≈ 138.25

Therefore, it will take approximately n/12 = 11.54 years to pay off the loan.

The closest option is C) 11.58 years.

You Recently Graduated and Borrowed $10,000 from You Parents