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 number of deposits:** Deposits for 4 years monthly: $n = 4 \times 12 = 48$ 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, amount grows with compound interest:** Number of months = 12 $$A_5 = A_4 \times (1 + r)^{12} = 20797.74 \times 1.015^{12}$$ Calculate $1.015^{12}$: $$1.015^{12} \approx 1.195618$$ So, $$A_5 = 20797.74 \times 1.195618 = 24870.44$$ 7. **Calculate total amount deposited:** $$300 \times 48 = 14400$$ 8. **Calculate interest earned:** $$\text{Interest} = A_5 - \text{Total deposits} = 24870.44 - 14400 = 10470.44$$ **Final answers:** - Amount at end of 5 years: $24870.44$ - Interest earned: $10470.44$