Question

Find the PV of $500 due in the future under each of these conditions

a. 12% nominal rate, semiannual compounding, discounted back 5 years
b. 12% nominal rate, quarterly compounded, discounted back 5 years
c. 12% nominal rate, monthly compounding, discounted back 1 year.
d. why do the differences in the PV's occur?

Answer 1

The PV of $500 due in the future varies based on the compounding frequency of a 12% nominal interest rate over different time periods. It decreases with more compounding periods due to an increase in the effective interest rate.

Step-by-step explanation:

The present value (PV) of $500 due in the future under different compounding conditions can be found using the present value formula PV = FV / (1 + r/n)nt, where FV is the future value, r is the nominal annual interest rate, n is the number of compounding periods per year, and t is the number of years.

• a. For a 12% nominal rate with semiannual compounding over 5 years, the formula becomes PV = 500 / (1 + 0.12/2)2*5.
• b. With a 12% nominal rate quarterly compounded over 5 years, the formula is PV = 500 / (1 + 0.12/4)4*5.
• c. For a 12% nominal rate with monthly compounding over 1 year, PV = 500 / (1 + 0.12/12)12*1.

The differences in the PVs occur because the frequency of compounding affects the amount of interest accumulated over time. More frequent compounding periods result in a higher effective interest rate, which in turn reduces the present value of the future amount.