1. **State the problem:** Calculate the final accumulated amount and total interest for $30,000 invested at 4% annual interest compounded quarterly for 2 years. 2. **Formula used:** The compound interest formula is $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the accumulated amount (principal + interest), - $P$ is the principal amount, - $r$ is the annual interest rate (decimal), - $n$ is the number of times interest is compounded per year, - $t$ is the time in years. 3. **Identify values:** - $P = 30000$ - $r = 0.04$ - $n = 4$ (quarterly compounding) - $t = 2$ 4. **Calculate the accumulated amount:** $$A = 30000 \left(1 + \frac{0.04}{4}\right)^{4 \times 2} = 30000 \left(1 + 0.01\right)^8 = 30000 \times 1.01^8$$ 5. **Calculate $1.01^8$:** $$1.01^8 = 1.0828567059$$ 6. **Multiply to find $A$:** $$A = 30000 \times 1.0828567059 = 32485.701177$$ 7. **Round to nearest dollar:** $$A \approx 32486$$ 8. **Calculate total interest:** $$\text{Interest} = A - P = 32486 - 30000 = 2486$$ **Final answers:** - Final accumulated amount: $32486$ - Total interest earned: $2486$