1. **Problem Statement:** Calculate the compound interest on a principal amount of 5000 for 2 years at an annual interest rate of 6%, compounded monthly. 2. **Formula:** The compound interest formula when interest is compounded monthly is: $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where: - $A$ is the amount after interest - $P$ is the principal amount - $r$ is the annual interest rate (in decimal) - $n$ is the number of times interest is compounded per year (monthly means $n=12$) - $t$ is the time in years 3. **Substitute values:** $$ P = 5000, \quad r = 0.06, \quad n = 12, \quad t = 2 $$ 4. **Calculate:** $$ A = 5000 \left(1 + \frac{0.06}{12}\right)^{12 \times 2} = 5000 \left(1 + 0.005\right)^{24} = 5000 \times (1.005)^{24} $$ 5. **Evaluate:** Calculate $ (1.005)^{24} $: $$ (1.005)^{24} \approx 1.12749 $$ 6. **Final amount:** $$ A = 5000 \times 1.12749 = 5637.45 $$ 7. **Compound interest earned:** $$ \text{Interest} = A - P = 5637.45 - 5000 = 637.45 $$ **Answer:** The compound interest earned after 2 years, compounded monthly, is approximately 637.45.