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:
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
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