Question

Ellen borrowed $25,000 from a loan shark at the APR of 35%, compounded monthly. The entire amount, principal plus interest, is to be repaid at the end of five years. This loan shark is not a nice person and Ellen is a little nervous, so she starts a savings account in her local bank. The bank pays interest at the APR of 8%, compounded quarterly. Ellen will make 20 equal quarterly deposits into her account, then, right after the last deposit, she will empty the account to repay the loan shark. How large do her quarterly payments need to be?

Answer 1

This question requires application of time value of money.

The amount borrowed PV = $25,000

Rate of Interest = 35% (annual) --> 2.917% (Monthly)

n = 5 years = 5 * 12 = 60 months

First we need to calculate the FV of this amount

FV = PV * (1 + r)ⁿ

FV = 25000 * (1 + 2.917%)⁶⁰

FV = $140,308.09

Now, Ellen starts making quarterly payments.

Future value of annuity is mathematically represented as:

FV = $140,308.09, r = 8% per year --> 2% per quarter, n = 5 * 4 quarters = 20 quarters

Substituting values in formula, we get:

P = $5,774.62. Quarterly payment that should be made by Ellen in her savings bank account