1. **State the problem:** We need to find the compound interest on 160000 for 1 year at an annual interest rate of 20%, compounded quarterly. 2. **Identify the formula for compound interest:** $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount after interest - $P$ is the principal (160000) - $r$ is the annual interest rate (20% = 0.20) - $n$ is the number of times interest is compounded per year (quarterly means $n=4$) - $t$ is the time in years (1 year) 3. **Substitute the values:** $$ A = 160000 \left(1 + \frac{0.20}{4}\right)^{4 \times 1} = 160000 \left(1 + 0.05\right)^4 = 160000 \times (1.05)^4 $$ 4. **Calculate $(1.05)^4$:** $$ (1.05)^4 = 1.21550625 $$ 5. **Calculate the amount $A$:** $$ A = 160000 \times 1.21550625 = 194480.99999999998 \approx 194481 $$ 6. **Calculate the compound interest:** $$ \text{Compound Interest} = A - P = 194481 - 160000 = 34481 $$ **Final answer:** The compound interest is 34481.