PSAT Math Multiple-Choice Question 825: Answer and Explanation

Question: 825

Bob deposits x dollars into his savings account on January 1, 2015, and the account grows at a constant annual rate of 3%, compounded annually. Assuming that Bob makes no deposits or withdrawals and that there are no account fees or other charges, what will be the amount of dollars in his account on January 1, 2017?

• A. 0.06x
• B. 1.06x
• C. 1.0609x
• D. 1.092727x

Correct Answer: C

Explanation:

(C) To determine a 3% increase on an original amount of x, add 3% to the original amount:

x + 0.03x = 1.03x

You can save time if you recognize that you can simply multiply x by 1.03 to determine the total of x plus 3% interest. The amount in the account is compounded twice. So multiply x by 1.03 twice:

x · 1.03 · 1.03 = 1.0609x