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If you invest $100 each month into an account earning 3% compounded monthly, how long will it take the account to grow to $20,000?

A. 36 months
B. 48 months
C. 60 months
D. 72 months

Answer :

Final answer:

Compound interest formula was used to calculate the time needed for an investment to grow to a certain amount with monthly contributions and a monthly compounding rate of 3%, resulting in a time period of 72 months. so, the correct answer d) 72 months.

Explanation:

The future value of an annuity formula is FV = P * [((1 + r)^nt - 1) / r], where FV is the future value, P is the payment per period, r is the interest rate per period, n is the number of compounds per period, and t is the time in years. However, since the compound interest in this scenario is applied monthly, we will adjust r and n accordingly. In this case:

P = $100 (monthly investment)

r = 0.03/12 (monthly interest rate)

n = 12 (number of times the interest is compounded per year)

FV = $20,000 (target amount)

Compound interest is calculated using the formula A = P(1 + r/n)nt, where A is the amount of money accumulated after n months or years, r is the annual interest rate (in decimal form), and t is the time the money is invested for. In this case, with $100 monthly investment at 3% compounded monthly, we want to find out when the account reaches $20,000. So, we have $20,000 = 100(1 + 0.03/12)12t, and solving for t gives us 72 months or 6 years, making the correct answer d) 72 months.

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Rewritten by : Barada