Mariah is putting $5,270 into an account earning 3.75% interest compounded quarterly. She estimates that it will take just over 9 years for this investment to grow to $8,000. Which of the following is a true statement?
Answer
A
Mariah’s estimate of the time is too low.
B
Mariah’s estimate of the time is correct.
C
Mariah’s estimate of the time is too high.
D
Mariah does not have enough information to estimate the time.
Explanation
Use the compound-interest formula: 8,000 = 5,270(1 + 0.0375/4)^(4t). Solving gives t = ln(8,000/5,270) ÷ [4 ln(1.009375)] ≈ 11.2 years. Since that is substantially longer than just over 9 years, Mariah’s estimate is too low: choice a.
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