Digital PSAT Math Practice Question 205: Answer and Explanation

Question: 205

The amount of money (A) in a bank account after a principal amount (P) is on deposit for t years at an annual interest rate r compounded n times per year is given by this equation:

Suppose that a banker would like to determine how changes in these variables would cause the bank to pay less interest to its clients. Which of the variables P, r, n, and t, if minimized, would cause less interest paid to clients?

• A. P only
• B. r and t only
• C. n and t only
• D. P, r, n, and t

Correct Answer: D

Explanation:

(D) Minimizing all of the variables will decrease the amount of money in the account after a given period of time. While you could plug in a variety of sample values and test the impact of changing each variable on the overall amount of money in the account, this is easier to simply think through using common sense. If you start off with less money, have a lower interest rate, and have less frequent compounding of interest, there will be less money in the account.