Final answer:
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.