Question

At the end of each month, Terry deposits $100 in a savings account at 6% annual interest compounded monthly. The balance after the twelfth payment is most nearly:

A) $1,268.25
B) $1,306.85
C) $1,321.93
D) $1,363.10

Answer 1

To calculate the balance after twelve payments, we can use the formula for compound interest. The balance after the twelfth payment is nearly $1,268.25. The option (A) is correct.

Step-by-step explanation:

To calculate the balance after twelve payments, we can use the formula for compound interest. The formula is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal (the initial amount deposited), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.

In this case, the principal is $100, the annual interest rate is 6% (or 0.06 as a decimal), and the interest is compounded monthly, so n = 12. The number of years is 1, because Terry makes monthly deposits for one year. Plugging these values into the formula, we have A = 100(1 + 0.06/12)^(12*1). Evaluating this expression gives us ≈ $1,268.25. Therefore, the balance after the twelfth payment is nearly $1,268.25 (Option A).