Final answer:
The future value of the annuity after 18 years, with a 5.9% interest rate compounded monthly and $54 monthly payments, is approximately $24,223.37. The value is calculated using the future value of an annuity formula.
Step-by-step explanation:
The student's question involves calculating the future value of an annuity with monthly contributions and compound interest. To find the total value of the annuity after 18 years with 5.9% interest compounded monthly and $54 monthly payments, we use the future value of an annuity formula:
- FV = P × [((1 + r)^n - 1) / r]
Where:
- FV is the future value of the annuity.
- P is the monthly payment, which is $54.
- r is the monthly interest rate (annual rate/12), which is (5.9%/12) or 0.00491667.
- n is the total number of payments (months), which is 18 years × 12 months/year = 216 months.
The calculation is as follows:
- FV = 54 × [((1 + 0.00491667)^216 - 1) / 0.00491667]
- FV = 54 × [(1.00491667^216 - 1) / 0.00491667]
- FV = 54 × [(3.19936791 - 1) / 0.00491667]
- FV = 54 × 448.580939
- FV = $24,223.370914
The future value of the annuity after 18 years is approximately $24,223.37.