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 the balance at the end of 15 years and the interest earned. 2. **Identify the type of problem:** This is an annuity problem with monthly payments but interest compounded annually. We assume payments accumulate without interest during the year and interest is applied once per year. 3. **Calculate total number of payments:** $$n = 15 \times 12 = 180 \text{ payments}$$ 4. **Calculate the future value of the annuity:** Since interest is compounded annually, we consider yearly contributions. Total yearly contribution: $$500 \times 12 = 6000$$ 5. **Use the future value of an ordinary annuity formula for yearly contributions:** $$FV = P \times \frac{(1 + r)^t - 1}{r}$$ where $P = 6000$ (annual payment), $r = 0.0475$ (annual interest rate), $t = 15$ years. 6. **Calculate:** $$FV = 6000 \times \frac{(1 + 0.0475)^{15} - 1}{0.0475}$$ Calculate $(1 + 0.0475)^{15}$: $$1.0475^{15} \approx 2.0006$$ So, $$FV = 6000 \times \frac{2.0006 - 1}{0.0475} = 6000 \times \frac{1.0006}{0.0475} \approx 6000 \times 21.06 = 126360$$ 7. **Calculate total amount saved without interest:** $$Total\,payments = 500 \times 180 = 90000$$ 8. **Calculate interest earned:** $$Interest = FV - Total\,payments = 126360 - 90000 = 36360$$ 9. **Round to nearest cent:** Balance: 126360.00 Interest earned: 36360.00 **Final answers:** - Balance at end: $126360.00$ - Interest earned: $36360.00$