1. **Problem statement:** Claudia deposits 300 every month into an account with 18% annual interest compounded monthly. Deposits are made for 4 years, then no more deposits for 1 year. Find the amount at the end of 5 years and the interest earned. 2. **Formula for future value of an annuity with monthly compounding:** $$A = P \times \frac{(1 + r)^n - 1}{r}$$ where $P$ is the monthly deposit, $r$ is the monthly interest rate, and $n$ is the total number of deposits. 3. **Calculate monthly interest rate:** Annual rate = 18% = 0.18 Monthly rate $r = \frac{0.18}{12} = 0.015$ 4. **Calculate total deposits for 4 years:** Number of months $n = 4 \times 12 = 48$ 5. **Calculate amount after 4 years of deposits:** $$A_{4} = 300 \times \frac{(1 + 0.015)^{48} - 1}{0.015}$$ Calculate $(1 + 0.015)^{48}$: $$ (1.015)^{48} \approx 2.039887 $$ So, $$A_{4} = 300 \times \frac{2.039887 - 1}{0.015} = 300 \times \frac{1.039887}{0.015} = 300 \times 69.3258 = 20797.74$$ 6. **No more deposits for 1 year, so amount grows with compound interest:** Number of months = 12 7. **Calculate amount after 5 years:** $$A_{5} = A_{4} \times (1 + 0.015)^{12}$$ Calculate $(1.015)^{12}$: $$ (1.015)^{12} \approx 1.195618 $$ So, $$A_{5} = 20797.74 \times 1.195618 = 24870.44$$ 8. **Calculate total amount deposited:** $$Total\ deposits = 300 \times 48 = 14400$$ 9. **Calculate interest earned:** $$Interest = A_{5} - Total\ deposits = 24870.44 - 14400 = 10470.44$$ **Final answers:** - Amount at end of 5 years: $24870.44$ - Interest earned: $10470.44$