Simple Interest Rate 5246A6

1. **State the problem:** We need to find the rate of simple interest that will make ₱7500 earn ₱2050 in 3 years and 4 months. 2. **Given:** - Principal, $P = 7500$ - Interest, $I = 2050$ - Time, $T = 3$ years and $4$ months = $3 + \frac{4}{12} = 3 + \frac{1}{3} = \frac{10}{3}$ years 3. **Formula for simple interest:** $$I = P \times R \times T$$ where $R$ is the rate per year (in decimal form). 4. **Rearrange the formula to solve for $R$:** $$R = \frac{I}{P \times T}$$ 5. **Substitute the known values:** $$R = \frac{2050}{7500 \times \frac{10}{3}}$$ 6. **Calculate the denominator:** $$7500 \times \frac{10}{3} = 7500 \times 3.3333 = 25000$$ 7. **Calculate $R$:** $$R = \frac{2050}{25000} = 0.082$$ 8. **Convert $R$ to percentage:** $$R = 0.082 \times 100 = 8.2\%$$ **Final answer:** The rate of simple interest is $8.2\%$ per year.