1. **State the problem:** We want to find how many years it takes for an investment to grow to a future value of 2300 with an interest rate of 5% and an interest earned of 300. 2. **Identify given values:** - Future value, $A = 2300$ - Interest rate, $r = 0.05$ - Interest earned = $300$ 3. **Find the principal $P$:** Since interest earned is $300$, and $A = P + \text{interest}$, we have $$P = A - 300 = 2300 - 300 = 2000$$ 4. **Use the compound interest formula:** $$A = P(1 + r)^n$$ where $n$ is the number of years. 5. **Plug in known values:** $$2300 = 2000(1 + 0.05)^n$$ 6. **Simplify:** $$\frac{2300}{2000} = 1.05^n$$ $$1.15 = 1.05^n$$ 7. **Solve for $n$ using logarithms:** $$n = \frac{\log(1.15)}{\log(1.05)}$$ 8. **Calculate:** $$n \approx \frac{0.0607}{0.0212} \approx 2.86$$ 9. **Interpretation:** It takes approximately 2.86 years to reach a future value of 2300 with a 5% interest rate and 300 interest earned.