1. **State the problem:** A man borrowed 8000 with a 5.5% interest charged in advance, receiving 7650. We need to find when the loan will be due. 2. **Formula and explanation:** Interest in advance means the interest is deducted from the principal before the borrower receives the money. The formula for interest in advance is: $$\text{Amount received} = \text{Principal} - \text{Interest}$$ where $$\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}$$ 3. **Set up the equation:** $$7650 = 8000 - 8000 \times 0.055 \times t$$ 4. **Solve for time $t$:** $$7650 = 8000 - 440t$$ $$440t = 8000 - 7650$$ $$440t = 350$$ $$t = \frac{350}{440} = 0.7955 \text{ years}$$ 5. **Convert time to months:** $$0.7955 \times 12 = 9.55 \text{ months}$$ **Final answer:** The loan will be due in approximately 9.55 months.