Question

select the statement that correctly explains the relationship between interest rates and present or future value.

assuming other variables stay the same, if the interest rate decreases, the present value of an investment decreases.

the interest rate and the present value of an investment are inversely related.

assuming other variables stay the same, if the interest rate decreases, the future value of an investment increases.

more time passes, the future value of an investment increases if the present value stays constant.

Explanation:

To determine the correct statement, we analyze the relationship between interest rates, present value (PV), and future value (FV) using financial concepts:

1. For the first option: The formula for present value is \( PV=\frac{FV}{(1 + r)^n} \) (or for an annuity, similar inverse - relationship with \( r \)). If \( r \) (interest rate) decreases, \( (1 + r)^n \) decreases, so \( PV=\frac{FV}{(1 + r)^n} \) should increase (not decrease). Thus, this option is wrong.

1. For the second option: From \( PV=\frac{FV}{(1 + r)^n} \), as \( r \) (interest rate) increases, \( PV \) decreases, and as \( r \) decreases, \( PV \) increases. This shows an inverse relationship between the interest rate and the present value of an investment.

1. For the third option: The future - value formula is \( FV = PV(1 + r)^n \). If \( r \) (interest rate) decreases, \( (1 + r)^n \) decreases, so \( FV \) should decrease (not increase). Thus, this option is wrong.

1. For the fourth option: The question is about the relationship between interest rates and present/future value, while this option is about the relationship between time and future value. So it is irrelevant to the question.

Answer:

The interest rate and the present value of an investment are inversely related.