Simple Interest Rate E5817C

1. **State the problem:** We need to find the rate of simple interest $r$ that will make ₱7500 earn ₱2050 in 3 years and 4 months. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is the interest earned, $P$ is the principal, $r$ is the rate per year (in decimal), and $t$ is the time in years. 3. **Convert time to years:** 3 years and 4 months = $3 + \frac{4}{12} = 3 + \frac{1}{3} = \frac{10}{3}$ years. 4. **Plug in known values:** $$2050 = 7500 \times r \times \frac{10}{3}$$ 5. **Solve for $r$:** $$r = \frac{2050}{7500 \times \frac{10}{3}} = \frac{2050}{7500 \times \frac{10}{3}}$$ 6. **Simplify denominator:** $$7500 \times \frac{10}{3} = 7500 \times \frac{10}{3} = \frac{7500 \times 10}{3} = \frac{75000}{3}$$ 7. **Calculate $r$:** $$r = \frac{2050}{\frac{75000}{3}} = 2050 \times \frac{3}{75000} = \frac{6150}{75000}$$ 8. **Simplify fraction:** $$r = \frac{6150}{75000} = \frac{\cancel{6150}}{\cancel{75000}} = \frac{41}{500} = 0.082$$ 9. **Convert to percentage:** $$r = 0.082 \times 100 = 8.2\%$$ **Final answer:** The rate of simple interest is $8.2\%$ per year.