Question

# Present Value for Various Compounding Periods Find the present value of \$500 due in the future...

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.

\$

. 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.

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