1. **State the problem:** We need to find the compound amount $A$ using the compound interest formula given the principal $P=1000$, annual interest rate $r=1\%$, number of compounding periods per year $m=4$, and total number of years $n=16$. 2. **Formula used:** The compound amount formula is $$A = P \left(1 + \frac{r}{100m}\right)^{mn}$$ where $r$ is in percent, so we divide by 100 to convert to decimal. 3. **Substitute the values:** $$A = 1000 \left(1 + \frac{1}{100 \times 4}\right)^{4 \times 16} = 1000 \left(1 + 0.0025\right)^{64}$$ 4. **Simplify inside the parentheses:** $$1 + 0.0025 = 1.0025$$ 5. **Calculate the exponent:** $$A = 1000 \times (1.0025)^{64}$$ 6. **Evaluate the power:** Using a calculator, $$(1.0025)^{64} \approx 1.16986$$ 7. **Calculate the final amount:** $$A = 1000 \times 1.16986 = 1169.86$$ **Final answer:** The compound amount after 16 years is approximately $1169.86$.