1. **State the problem:** We need to find the amount owed after 10 years on a loan of 2000 at an 18% annual interest rate, compounded quarterly. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount owed 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:** - $P = 2000$ - $r = 0.18$ - $n = 4$ (quarterly compounding) - $t = 10$ 4. **Substitute values into the formula:** $$A = 2000 \left(1 + \frac{0.18}{4}\right)^{4 \times 10} = 2000 \left(1 + 0.045\right)^{40} = 2000 \times 1.045^{40}$$ 5. **Calculate the power:** $$1.045^{40} \approx 5.006577$$ 6. **Calculate the final amount:** $$A = 2000 \times 5.006577 = 10013.15$$ 7. **Answer:** The amount owed after 10 years is approximately **10013.15**. This means the loan grows to 10013.15 after 10 years with quarterly compounding at 18% interest.