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