1. **Problem statement:** Nakesa deposited an amount $P$ in a bank for 2 years. The bank offers two types of interest rates: simple interest (SI) at 5% per annum and compound interest (CI) at 5% per annum. The difference in interest earned between CI and SI after 2 years is 210. We need to find the principal amount $P$. 2. **Formulas used:** - Simple Interest: $SI = P \times r \times t$ - Compound Interest: $CI = P \times (1 + r)^t - P$ where $P$ is the principal, $r$ is the rate per annum (in decimal), and $t$ is the time in years. 3. **Given:** - $r = 5\% = 0.05$ - $t = 2$ years - Difference $CI - SI = 210$ 4. **Calculate Simple Interest:** $$SI = P \times 0.05 \times 2 = 0.1P$$ 5. **Calculate Compound Interest:** $$CI = P \times (1 + 0.05)^2 - P = P \times (1.1025) - P = 0.1025P$$ 6. **Set up the equation for the difference:** $$CI - SI = 0.1025P - 0.1P = 0.0025P = 210$$ 7. **Solve for $P$:** $$P = \frac{210}{0.0025} = 84000$$ **Final answer:** The principal amount $P$ is 84000.