Question

Find the present value of $600 due in the future under each of the following conditions.

12% nominal rate, semiannual compounding, discounted back 5 years.

12% nominal rate, quarterly compounding, discounted back 5 years.

12% nominal rate, monthly compounding, discounted back 1 year

Answer 1

Part 1: 12% nominal rate, semiannual compounding, discounted back 5 years.

r = 12%/2 = 6% (semi-annual), n = 5 * 2 = 10 semi-annual periods.

$600 = PV * (1 + 6%)¹⁰

$600 = PV * 1.790848

PV = $335.04

Part 2: 12% nominal rate, quarterly compounding, discounted back 5 years.

r = 12%/4 = 3% (quarterly), n = 5 * 4 = 20 quarterly periods.

$600 = PV * (1 + 3%)²⁰

$600 = PV * 1.806111

PV = $332.21

Part 3: 12% nominal rate, monthly compounding, discounted back 1 year

r = 12%/12 = 1% (monthly), n = 1 * 12 = 12 monthly periods.

$600 = PV * (1 + 1%)¹²

$600 = PV * 1.126825

PV = $532.47