1. **State the problem:** We have two accounts: Account A with simple interest of 0.1% per month and Account B with compound interest of 1.5% per year. We want to find: - How many months for Account A's investment of 30000 to reach 31200. - Which account yields more interest after 3 years. 2. **Formulas:** - Simple interest: $$A = P(1 + rt)$$ where $P$ is principal, $r$ is rate per time period, $t$ is number of periods. - Compound interest: $$A = P(1 + r)^t$$ where $r$ is rate per compounding period, $t$ is number of periods. 3. **Calculate months for Account A:** - Given $P=30000$, $A=31200$, $r=0.1\% = 0.001$ per month. - Use formula: $$31200 = 30000(1 + 0.001t)$$ - Divide both sides by 30000: $$1.04 = 1 + 0.001t$$ - Subtract 1: $$0.04 = 0.001t$$ - Solve for $t$: $$t = \frac{0.04}{0.001} = 40$$ months. 4. **Calculate amount for Account B after 3 years:** - Given $P=30000$, $r=1.5\% = 0.015$ per year, $t=3$ years. - Use formula: $$A = 30000(1 + 0.015)^3$$ - Calculate: $$A = 30000(1.015)^3 = 30000 \times 1.04568 = 31370.4$$ approximately. 5. **Calculate amount for Account A after 3 years (36 months):** - Use simple interest formula: $$A = 30000(1 + 0.001 \times 36) = 30000(1 + 0.036) = 30000 \times 1.036 = 31080$$. 6. **Compare amounts after 3 years:** - Account A: 31080 - Account B: 31370.4 **Conclusion:** - It takes 40 months for Account A to reach 31200. - After 3 years, Account B provides more interest than Account A. **Final answers:** - Months for Account A to reach 31200: $40$ - Account B yields more interest after 3 years.