Question

1. You set up a college fund in which you pay $2500 each year at the end of the year. How much money will you have accumulated in the fund after 10 years, if your fund earns 13% compounded annually?

Your Answer:

2. Lauren knows she can afford to make monthly payments of $300 for 36 months. How much will the bank lend her today on a 3% APR car loan in exchange for her promised monthly payments?

Your Answer:

3. Your bank offers you a 60-month, 3% APR car loan for a $60000 new Mercedes SLK300 Roadster. What will your monthly payment be?

Your Answer:

Answer 1

1). FV of Annuity = Annual Payment * [{(1 + r)ⁿ - 1} / r]

= $2500 * [{(1 + 0.13)¹⁰ - 1} / 0.13]

= $2500 * [2.3946 / 0.13]

= $2500 * 18.4197

= $46,049.37

2). PV of Annuity = Monthly Payment * [{1 - (1 + r)^-n} / r]

= $300 * [{1 - (1 + 0.03/12)^-36} / (0.03/12)]

= $300 * [0.0860 / 0.0025]

= $300 * 34.3865

= $10,315.94

3). Monthly Payment = [Loan Amount * r] / [1 - (1 + r)^-n]

= [$60,000 * (0.03/12)] / [1 - (1 + 0.03/12)^-60]

= $150 / 0.1391 = $1,078.12