question 19 a two - year investment of $3500 is made today at an annual interest rate of 5.75%. which of the…

Explanation:

Step1: Recall future - value formula

The future - value formula is $FV = PV(1 + r)^n$, where $FV$ is the future value, $PV$ is the present value, $r$ is the interest rate per period, and $n$ is the number of periods. For a fixed present value $PV$ and number of periods $n$, the future value $FV$ is directly related to the interest rate $r$. As $r$ increases, $(1 + r)^n$ increases, and so does $FV$.

Step2: Analyze present - value formula

The present - value formula is $PV=\frac{FV}{(1 + r)^n}$. For a fixed future value $FV$ and number of periods $n$, the present value $PV$ is inversely related to the interest rate $r$. As $r$ increases, $(1 + r)^n$ increases, and $PV$ decreases.

Step3: Evaluate each option

• Option A: Higher interest rate leads to higher future value. This is correct as per the future - value formula.
• Option B: Higher interest rate leads to lower present value, not higher present value.
• Option C: Lower interest rate leads to lower future value (since $FV = PV(1 + r)^n$), not higher future value.
• Option D: Future value is directly related to the interest rate, so it changes as the interest rate changes.

Answer:

A. The future value would be greater if the interest rate was higher