Subjects algebra

Simple Interest 454C96

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1. **State the problem:** Margo borrows 700 and agrees to pay 8% annual interest after 7 months. We need to find the interest she will pay. 2. **Formula used:** The simple interest formula is $$I = P \times r \times t$$ where: - $I$ is the interest - $P$ is the principal amount (700) - $r$ is the annual interest rate (8% or 0.08) - $t$ is the time in years 3. **Convert time to years:** Since 7 months is $$\frac{7}{12}$$ years, we have $$t = \frac{7}{12}$$. 4. **Calculate interest:** $$I = 700 \times 0.08 \times \frac{7}{12}$$ 5. **Simplify step-by-step:** $$I = 700 \times 0.08 \times \frac{7}{12} = 700 \times \frac{8}{100} \times \frac{7}{12}$$ 6. **Multiply numerators and denominators:** $$I = 700 \times \frac{8 \times 7}{100 \times 12} = 700 \times \frac{56}{1200}$$ 7. **Simplify fraction:** $$\frac{56}{1200} = \frac{56 \div 8}{1200 \div 8} = \frac{7}{150}$$ 8. **Calculate final interest:** $$I = 700 \times \frac{7}{150} = \frac{700 \times 7}{150}$$ 9. **Simplify numerator and denominator:** $$I = \frac{4900}{150}$$ 10. **Divide:** $$I = 32.666\ldots$$ 11. **Round to nearest cent:** $$I = 32.67$$ **Final answer:** Margo will pay **32.67** in interest.