1. **State the problem:** Lucy deposited 4000 into an account with 2.1% annual interest compounded monthly. We want to find the amount after 7 years. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after time $t$, - $P$ is the principal (initial amount), - $r$ is the annual interest rate (decimal), - $n$ is the number of compounding periods per year, - $t$ is the time in years. 3. **Identify values:** - $P = 4000$ - $r = 0.021$ (2.1% as decimal) - $n = 12$ (monthly compounding) - $t = 7$ 4. **Substitute values:** $$A = 4000 \left(1 + \frac{0.021}{12}\right)^{12 \times 7}$$ 5. **Calculate inside the parentheses:** $$1 + \frac{0.021}{12} = 1 + 0.00175 = 1.00175$$ 6. **Calculate the exponent:** $$12 \times 7 = 84$$ 7. **Calculate the power:** $$1.00175^{84}$$ 8. **Calculate the amount:** $$A = 4000 \times 1.00175^{84}$$ Using a calculator: $$1.00175^{84} \approx 1.158924$$ So, $$A = 4000 \times 1.158924 = 4635.696$$ 9. **Round to nearest cent:** $$A \approx 4635.70$$ **Final answer:** Lucy will have approximately **4635.70** in the account after 7 years.