A private investor loans $4,500 to a new business at an annual interest rate of % for 8 years. How much interest will the investor earn after those 8 years?

Sure, let's solve this step by step.

1. Identify the principal amount (P), which is the initial amount of the loan. $P = \$4,500$

2. Identify the annual interest rate (r). Since the rate is not specified in the question, let's assume it is $r \%$.

3. Identify the time period (t) in years. $t = 8$ years

4. Use the formula for simple interest, which is: $I = P \times r \times t$

5. Substitute the given values into the formula: $I = 4500 \times \frac{r}{100} \times 8$

6. Simplify the expression: $I = 4500 \times \frac{8r}{100}$ $I = 4500 \times \frac{2r}{25}$ $I = 360r$

So, the interest earned after 8 years is $360r$ dollars, where $r$ is the annual interest rate in percentage.