The present value of $400 discounted at a 15% nominal rate varies with the compounding frequency: $127.99 semiannually, $123.48 quarterly, and $349.14 monthly. This demonstrates how compounding affects the present value calculation.
The present value of $400 due in the future at a nominal rate of 15% under various compounding conditions can be calculated using the present value formula: PV = FV / (1 + r/n)^(nt), where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.
- (a) For semiannual compounding, n equals 2: PV = $400 / (1 + 0.15/2)^(2*7).
- (b) For quarterly compounding, n equals 4: PV = $400 / (1 + 0.15/4)^(4*7).
- (c) For monthly compounding, n equals 12: PV = $400 / (1 + 0.15/12)^(12*1).
In each scenario, calculating the PV using the appropriate formula yields:
- (a) $127.99
- (b) $123.48
- (c) $349.14
The differences in PV occur due to the frequency of compounding, which impacts how often interest is added to the principal.