1. **State the problem:** We need to find the simple interest rate for a 3-month loan of 4000 with a maturity value of 4085. 2. **Formula for simple interest:** $$\text{Maturity Value} = \text{Principal} + \text{Interest}$$ where $$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$ 3. **Identify known values:** - Principal, $P = 4000$ - Maturity Value, $A = 4085$ - Time, $T = \frac{3}{12} = 0.25$ years (since 3 months is a quarter of a year) - Rate, $R = ?$ 4. **Calculate interest:** $$I = A - P = 4085 - 4000 = 85$$ 5. **Use the interest formula to find rate:** $$I = P \times R \times T$$ $$85 = 4000 \times R \times 0.25$$ 6. **Solve for $R$:** $$R = \frac{85}{4000 \times 0.25}$$ 7. **Show cancellation:** $$R = \frac{85}{\cancel{4000} \times 0.25} = \frac{85}{1000}$$ 8. **Calculate $R$:** $$R = 0.085 = 8.5\%$$ **Final answer:** The simple interest rate is **8.5%**.