1. **State the problem:** Janet saves 500 at the beginning of every month for 15 years in a fund with an annual interest rate of 4.75% compounded annually. We need to find: a. The balance in the fund at the end of 15 years. b. The total interest earned over the period. 2. **Identify the type of problem:** This is an annuity problem with monthly payments but interest compounded annually. 3. **Convert the problem to annual terms:** Since interest compounds annually, we consider the total amount saved each year. Monthly saving = 500 Annual saving = 500 \times 12 = 6000 4. **Use the future value of an ordinary annuity formula:** $$FV = P \times \frac{(1 + r)^n - 1}{r}$$ where $P = 6000$ (annual payment), $r = 0.0475$ (annual interest rate), $n = 15$ (number of years). 5. **Calculate the future value:** $$FV = 6000 \times \frac{(1 + 0.0475)^{15} - 1}{0.0475}$$ Calculate $(1 + 0.0475)^{15}$: $$1.0475^{15} \approx 2.0004$$ Then, $$FV = 6000 \times \frac{2.0004 - 1}{0.0475} = 6000 \times \frac{1.0004}{0.0475} \approx 6000 \times 21.06 = 126360$$ 6. **Calculate total amount saved without interest:** $$\text{Total principal} = 6000 \times 15 = 90000$$ 7. **Calculate interest earned:** $$\text{Interest} = FV - \text{Total principal} = 126360 - 90000 = 36360$$ 8. **Round to nearest cent:** a. Balance = 126360.00 b. Interest earned = 36360.00 **Final answers:** - a. The balance in the fund at the end of 15 years is **126360.00**. - b. The interest earned over the period is **36360.00**.