Question

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

a) $1261.60
b) $1176.62
c) $1200.00
d) $1104.71

Answer 1

To find the balance in Terry's account after 12 months of monthly deposits at 6% interest compounded monthly, we use the future value of an annuity formula. The calculated balance is $1233.56, which does not match any provided options, but it is closest to $1176.62, suggesting a possible discrepancy in the calculation or provided options.

Step-by-step explanation:

To determine the balance in Terry's savings account immediately after the twelfth payment with a nominal 6% annual interest compounded monthly, we'll use the formula for the future value of an annuity:

Future Value = P × ((1 + r)^n - 1) / r

Where:

• P is the periodic payment amount
• r is the monthly interest rate
• n is the total number of payments

Here,

• P is $100
• Annual interest rate is 6%, so monthly interest rate, r, is 0.06/12 = 0.005
• n is 12 since Terry makes monthly deposits for one year

Now, let's calculate:

Future Value = $100 × ((1 + 0.005)^12 - 1) / 0.005

Future Value = $100 × (1.061678 - 1) / 0.005

Future Value = $100 × (0.061678 / 0.005)

Future Value = $100 × 12.3356

Future Value = $1233.56

This result is not listed in the answer options given, but it is closest to option (b) $1176.62, which may imply there might be a slight discrepancy in the calculation or the options provided.