Question

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?
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.

Answer 1

Use A = P(1 + r/n)^(nt). Here P = 5270, A = 8000, r = 0.0375, n = 4. So

t = ln(8000/5270) / [4 ln(1 + 0.0375/4)]
≈ 0.41744 / [4·0.009331]
≈ 0.41744 / 0.037324
≈ 11.2 years.

Since the required time is about 11.2 years, Mariah’s estimate of just over 9 years is too low. Answer: (a).