1. **State the problem:** Calculate the interest earned on a $3100 investment at 5.91% annual interest compounded monthly for 5 years. 2. **Formula used:** Compound interest formula is $$A = P\left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount after interest - $P$ is the principal (initial investment) - $r$ is the annual interest rate (decimal) - $n$ is the number of times interest is compounded per year - $t$ is the time in years 3. **Plug in values:** $$P = 3100, r = 0.0591, n = 12, t = 5$$ 4. **Calculate:** $$A = 3100\left(1 + \frac{0.0591}{12}\right)^{12 \times 5} = 3100\left(1 + 0.004925\right)^{60} = 3100(1.004925)^{60}$$ 5. **Evaluate power:** $$1.004925^{60} \approx 1.349353$$ 6. **Calculate amount:** $$A = 3100 \times 1.349353 = 4182.995$$ 7. **Calculate interest earned:** $$\text{Interest} = A - P = 4182.995 - 3100 = 1082.995$$ 8. **Round to nearest cent:** $$\boxed{1083.00}$$ --- 1. **State the problem:** Find the interest earned on a $5200 investment at a simple annual rate of 4.72% for 18 years. 2. **Formula used:** Simple interest formula is $$I = P \times r \times t$$ where: - $I$ is the interest - $P$ is the principal - $r$ is the annual interest rate (decimal) - $t$ is the time in years 3. **Plug in values:** $$P = 5200, r = 0.0472, t = 18$$ 4. **Calculate interest:** $$I = 5200 \times 0.0472 \times 18 = 5200 \times 0.8496 = 4417.92$$ 5. **Round to nearest cent:** $$\boxed{4417.92}$$