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

Tiulipe Penisoni · Accepted Answer

Final Answer : B, Explanation :  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 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

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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) 33B) 37C) 41D) 45

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Learning Objectives

Learning Objectives

Related questions

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