Question: Billy took out $15500 in student loans to pay for his schooling. If he must pay the loan back over 15 years at an annual interest rate of 4.75%, how much interest will he end up paying on this loan if he pays it off on time?
1. **State the problem:**
Billy borrowed $15500$ at an annual interest rate of $4.75\%$ to be paid back over $15$ years. We need to find the total interest paid if he pays it off on time.
2. **Identify the formula:**
Since the problem does not specify compound interest, we assume simple interest. The formula for simple interest is:
$$I = P \times r \times t$$
where:
- $I$ is the interest,
- $P$ is the principal amount,
- $r$ is the annual interest rate (in decimal),
- $t$ is the time in years.
3. **Convert the interest rate to decimal:**
$$r = \frac{4.75}{100} = 0.0475$$
4. **Plug in the values:**
$$I = 15500 \times 0.0475 \times 15$$
5. **Calculate step-by-step:**
$$15500 \times 0.0475 = 736.25$$
$$736.25 \times 15 = 11043.75$$
6. **Interpretation:**
Billy will pay $11043.75$ in interest over the $15$ years if he pays the loan off on time.
**Final answer:**
$$\boxed{11043.75}$$