Question

Present Value for Various Compounding Periods

Find the present value of $500 due in the future under each of the following conditions. Do not round intermediate calculations. Round your answers to the nearest cent.

1. 9% nominal rate, semiannual compounding, discounted back 5 years.

   $  

2. 9% nominal rate, quarterly compounding, discounted back 5 years.

   $  

3. 9% nominal rate, monthly compounding, discounted back 1 year.

   $  

Answer 1

. present value of single amount = A / (1+r)^n

a. here,

A = $500

r= 9% per annum

=>9% * 6/12

=>4.5%

=>0.045.

n= 5 years.* 2 semi annual periods

=>10 semi annual periods.

present value = $500 / (1.045)^10

=>$321.96.

b.here,

A = 500

r = 9% per annum =>9%*3 months / 12 months

=>2.25%

=>0.0225.

n = 5 years * 4 quarters

=>20.

present value=>500 / (1.0225)^20.

=>$320.41.

c. A = 500.

r = 9% * 1/12 months

=>0.75% per month.

=>0.0075

n = 1 year * 12 months

=>12.

r = 500 / (1.0075)^12

=>$457.12.