Part 1A twominus−year investment of $3500 is made today at an annual interest rate of 5.75%. Which of the following statements is TRUE? Part 1
A. The present value would be greater if the interest rate was higher. B. The future value would be greater if the interest rate was higher. C. The future value would be greater if the interest rate was lower. D. The future value does not change as the interest rate changes.

Question

Part 1A twominus−year investment of​ $3500 is made today at an annual interest rate of​ 5.75%. Which of the following statements is​ TRUE? Part 1
A. The present value would be greater if the interest rate was higher. B. The future value would be greater if the interest rate was higher. C. The future value would be greater if the interest rate was lower. D. The future value does not change as the interest rate changes.

BlackTom AI · Accepted Answer

To tackle this problem, I’ll examine how present value and future value respond to changes in the interest rate, given an initial investment today of $3,500 at 5.75% per year.
Option A: The present value would be greater if the interest rate was higher. This is incorrect because present value is calculated by discounting future money back to today using the interest rate. A higher rate increases the discount, which reduces the present value, not increases it.
Option B: The future value would be greater if the interest rate was higher. This statement aligns with the time value of money: a higher interest rate compounds more money over the same period, so the amount accumulated in the future (the future value) rises as the rate rises.
Option C: The future value would be greater if the interest rate was lower. This is the opposite of the correct relationship. Lower rates yield less compounding, resulting in a smaller future value.
Option D: The future value does not change as the interest rate changes. This is false because the future value directly depends on the interest rate through compounding; changing the rate changes the amount accumulated in the future.
In summary, the only statement that correctly captures the effect of a higher interest rate on the investment’s future value is Option B, since higher rates increase the amount accrued over time due to compounding effects.

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