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
Simple Interest 2Aaf2B
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.