1. **Stating the problem:** Calculate the amount and compound interest for a principal sum after a certain time period with a given interest rate compounded annually. 2. **Formula used:** - Amount after $n$ years: $$A = P\left(1 + \frac{r}{100}\right)^n$$ - Compound Interest (CI): $$CI = A - P$$ where $P$ is the principal, $r$ is the annual interest rate (in %), and $n$ is the number of years. 3. **Explanation:** Compound interest means interest is calculated on the initial principal and also on the accumulated interest from previous periods. 4. **Example:** Suppose $P=1000$, $r=5\%$, and $n=3$ years. 5. Calculate amount: $$A = 1000 \times \left(1 + \frac{5}{100}\right)^3 = 1000 \times (1.05)^3 = 1000 \times 1.157625 = 1157.63$$ 6. Calculate compound interest: $$CI = 1157.63 - 1000 = 157.63$$ 7. **Answer:** The amount after 3 years is $1157.63$ and the compound interest earned is $157.63$.