1. **State the problem:** We want to find the rate of return $r$ for an investment where the initial amount is 6500 and the amount after 3 years is 8300. 2. **Formula used:** The future value formula for compound interest is $$FV = PV \times (1 + r)^t$$ where $FV$ is the future value, $PV$ is the present value, $r$ is the rate of return per period, and $t$ is the number of periods. 3. **Plug in the known values:** $$8300 = 6500 \times (1 + r)^3$$ 4. **Isolate $(1 + r)^3$:** $$\frac{8300}{6500} = (1 + r)^3$$ 5. **Simplify the fraction:** $$\frac{\cancel{8300}}{\cancel{6500}} = \frac{83}{65} = 1.276923... = (1 + r)^3$$ 6. **Take the cube root of both sides to solve for $1 + r$:** $$1 + r = \sqrt[3]{1.276923}$$ 7. **Calculate the cube root:** $$1 + r \approx 1.0849$$ 8. **Solve for $r$:** $$r = 1.0849 - 1 = 0.0849$$ 9. **Convert to percentage and round:** $$r \approx 8.49\%$$ **Final answer:** The rate of return is approximately **8.49%**.