Question

Present Value for Various Compounding Periods

Find the present value of $775 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

1. 15% nominal rate, semiannual compounding, discounted back 5 years.

   $  

2. 15% nominal rate, quarterly compounding, discounted back 5 years.

   $  

3. 15% nominal rate, monthly compounding, discounted back 1 year.

   $  

Answer 1

a) r = 15%/2 = 7.5% (semi-annually), n = 5 * 2 = 10 semi-annual periods

PV = $775/(1 + 7.5%)10

PV = $775/2.0160

PV = $376.02

b) r = 15%/4 = 3.75% (quarterly), n = 5 * 4 = 20 quarterly periods

PV = $775/(1 + 3.35%)20

PV = $775/2.0882

PV = $371.14

c) r = 15%/12 = 1.25% (monthly), n = 1 * 12 = 12 monthly periods

PV = $775/(1 + 1.25%)12

PV = $775/1.1608

PV = $667.67