The impact of interest rate changes in the PV of $100 due in 20 years compared to the PV of $100 due in one year are: a. smaller because interest rate changes have a greater impact on the near-term cash flows than distant cash flows.
b. the same because the cash flow is the same.
c. greater because interest rate changes have a greater impact on distant cash flows than near-term cash flows.
d. sometimes less and sometimes more depending on the interest rate.

c. greater because interest rate changes have a greater impact on distant cash flows than near-term cash flows.

Explanation:

Interest rate changes have a greater impact on distant cashflows because those cashflows will be exposed to the interest rates for longer. This means that they will be subjected to more discounting than a cashflow that is due in one year which would be subject to only a single year of discounting.

For instance, assume the required rate of return for two investments is 10%. One investment yields $10,000 in 20 years and another yields $10,000 in 2 years .

The present value of both are:

= 10,000 / (1 + 10%)²⁰                                                  = 10,000 / ( 1 + 10%)²

= $1,486.43                                                                  = $8,264.46

Notice the difference. The longer term investment was more exposed to interest rate effects.