Question

Which one of these statements is correct concerning the relationship of PV, FV, i, and N? Assume the interest rate is constant and positive

a. All else held constant, the longer the time period, the lower the future value
b. All else held constant, the longer the time period, the higher the interest rate
c. All else held constant, the longer the time period, the lower the current value
d. All else held constant, the shorter the time period, the lower the present value

Answer 1

The correct statement is that the longer the time period, the lower the future value.

Step-by-step explanation:

The correct statement concerning the relationship of PV (present value), FV (future value), i (interest rate), and N (time period) is: All else held constant, the longer the time period, the lower the future value (option a).

When considering the relationship between time period and future value, we can use the formula for present value (PV) to understand how changes in time period affect the future value (FV). According to the formula, PV = FV / (1 + i)^N, where i is the interest rate. As N (the time period) increases, the denominator (1 + i)^N becomes larger, resulting in a smaller PV and lower FV.

For example, let's say you have $100 and want to invest it for 5 years, with an annual interest rate of 5%. Using the formula, the present value of the investment would be $78.35, and the future value after 5 years would be $100. So, as the time period increases, the future value decreases.