You are considering investing in a bank account that pays a nominal annual rate of 6%, compounded monthly. If you invest $5,000 at the END of each month, how many months will it take for your account to grow to $200,000? Round fractional years up.
A) 33
B) 37
C) 41
D) 45

Question

Quizplus · Accepted Answer

We can use the formula for future value of an annuity to determine how many months it will take for the account to grow to $200,000:

FV = PMT * (((1 + r/n)^(n*t)) - 1) / (r/n)

where FV is the future value, PMT is the payment amount ($5,000), r is the nominal annual rate (6%), n is the number of compounding periods per year (12), and t is the number of years.

Simplifying and solving for t, we get:

t = log((FV * r/n + PMT) / PMT) / (n * log(1 + r/n))

Substituting in the given values, we get:

t = log((200000*0.06/12 + 5000) / 5000) / (12 * log(1 + 0.06/12))
t = 36.9

Therefore, it will take approximately 37 months for the account to grow to $200,000, rounded up to the nearest whole month. The correct answer is B.

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