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

The future value of an annuity is given by the formula:FV = P * [(1 + r/n)^(nt) - 1] / (r/n)where:P is the periodic paymentr is the annual interest raten is the number of compounding periods per yeart is the number of yearsIn this case, we have:P = $5,000r = 6% = 0.06n = 12 (monthly compounding)FV = $200,000Solving for t, we get:t = log(FV * (r/n) / (P * [(1 + r/n)^(nt) - 1])) / (n * log(1 + r/n))t = log(200000 * (0.06/12) / (5000 * [(1 + 0.06/12)^(12t) - 1])) / (12 * log(1 + 0.06/12))t = 37.03Rounding up, it will take 37 months for the account to grow to $200,000.

You Are Considering Investing in a Bank Account That Pays