Subjects finance

Simple Interest 2Aaf2B

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Dante borrows 5000 at a simple interest rate of 4% per year for 2.5 years. We need to find the interest if he pays back after 2.5 years, the interest if he pays back 9 months early, and the savings from early payment. 2. **Formula for simple interest:** $$I = P \times r \times t$$ where $I$ is interest, $P$ is principal, $r$ is annual interest rate (decimal), and $t$ is time in years. 3. **Calculate interest for 2.5 years:** $$I = 5000 \times 0.04 \times 2.5 = 5000 \times 0.1 = 500$$ 4. **Calculate interest if paid 9 months early:** 9 months = $\frac{9}{12} = 0.75$ years New time $t = 2.5 - 0.75 = 1.75$ years $$I = 5000 \times 0.04 \times 1.75 = 5000 \times 0.07 = 350$$ 5. **Calculate savings:** $$\text{savings} = 500 - 350 = 150$$ **Final answers:** - Interest if paid after 2.5 years: 500 - Interest if paid 9 months early: 350 - Savings by early payment: 150