PSAT Math Multiple-Choice Question 729: Answer and Explanation

Question: 729

Maria currently has $10,000 in her retirement fund. She wants to see how much money she will have in her fund for several different years in the future, assuming that her portfolio has a steady annual growth rate of 10%. What function f(n) would model the amount she should have in her portfolio in n years?

• A. f(n) = 10,000ⁿ
• B. f(n) = 10,000 × 0.1ⁿ
• C. f(n) = 10,000 × 1.1ⁿ
• D. f(n) = 10,000 × 1.11ⁿ

Correct Answer: C

Explanation:

(C) For each year she has the portfolio, its value increases 10%. Therefore, the amount after one year of growth over the original amount at the beginning of that year will be 1.1 times the original amount. This process will repeat for each year Maria has the portfolio growing at this rate, making f(n) = 10,000 × 1.1ⁿ.

You can also see this using concrete numbers. If Maria starts with $10,000, after 1 year, she will have 10% interest added to the original amount:

10% of 10,000 = 0.1 × 10,000 = 1,000

Then you can add 1,000 to the original 10,000 to have $11,000 after the first year. To see how much money Maria will have after two years, find 10% of this new total:

10% of 11,000 = 0.1 × 11,000 = 1,100

Then add this to the original 11,000 to find how much she will have in her account at the end of year 2:

11,000 + 1,100 = 12,100

The only option that fits these concrete numbers is choice (C).