Final answer:
The future value of Joanne's 30-year investment, with an annual contribution of $3,000 and an annual interest rate of 2.4% compounded quarterly, is approximately $132,040, rounded to the nearest dollar.
Step-by-step explanation:
The question involves calculating the future value of an investment with regular contributions and compound interest. Joanne contributes $3,000 yearly to an account with a 2.4% annual interest rate, compounded quarterly, for 30 years. To solve this, we need to use the future value of an annuity formula:
FV = P * { ({(1 + r/n)}^(nt) - 1) / (r/n) }
Where:
- P is the annual payment ($3,000)
- r is the annual interest rate (0.024)
- n is the number of compounding periods per year (4)
- t is the number of years the money is invested (30)
Calculating this gives:
FV = 3000 * { ({(1 + 0.024/4)}^(4*30) - 1) / (0.024/4) }
Now, we compute the future value, rounding to the nearest dollar.
This value turns out to be option B. $132,040, which can be further verified using a financial calculator or software capable of these calculations.