Final answer:
The future value of an account with a principal of $12,000 at an annual rate of 3% compounded monthly for 4 years is $13,513.92, which is not one of the listed options provided by the student.
Step-by-step explanation:
To determine the value of an account at the end of 4 years with a principal amount of $12,000, an annual interest rate of 3%, and monthly compounding interest, one would use the formula for computing future value using compound interest:
Future Value = Principal × (1 + interest rate) to the power of time
The monthly interest rate is the annual rate divided by 12, which in this case is 0.03/12. The number of times the interest is compounded per year is 12 (monthly), and the total number of times interest is compounded over the period is 12 times the number of years, which is 4 in this case. So:
Future Value = $12,000 × (1 + 0.03/12)(12×4)
Principal × (1 + interest rate)time
Let's calculate:
Future Value = $12,000 × (1 + 0.0025)48
Future Value = $12,000 × (1.0025)48
Future Value = $12,000 × 1.12616
Future Value = $13,513.92
Therefore, the future value of the account after 4 years is $13,513.92, which is not one of the provided options. This suggests an error in the answer choices provided by the student. Compound interest can make a significant difference with even modest sums of money and over a period as short as 4 years, as seen in the example of $100 gaining an extra $0.76 over three years as compared to simple interest.