1. **State the problem:** Calculate the future value of $1000 invested at different interest rates and time periods using compound interest. 2. **Formula used:** The compound interest formula is $$A = P(1 + r)^t$$ where: - $A$ is the amount after time $t$, - $P$ is the principal amount, - $r$ is the annual interest rate (decimal), - $t$ is the time in years. 3. **Calculate for $1000$ at 14% for 2 years:** $$A = 1000(1 + 0.14)^2 = 1000(1.14)^2 = 1000 \times 1.2996 = 1299.60$$ 4. **Calculate for $1000$ at 8% for 3 years:** $$A = 1000(1 + 0.08)^3 = 1000(1.08)^3 = 1000 \times 1.259712 = 1259.71$$ 5. **Calculate for $1000$ at 6% for 4 years:** $$A = 1000(1 + 0.06)^4 = 1000(1.06)^4 = 1000 \times 1.262476 = 1262.48$$ 6. **Calculate for $1000$ at 5% for 5 years:** $$A = 1000(1 + 0.05)^5 = 1000(1.05)^5 = 1000 \times 1.276282 = 1276.28$$ **Final answers:** - $1000$ at 14% for 2 years: $1299.60$ - $1000$ at 8% for 3 years: $1259.71$ - $1000$ at 6% for 4 years: $1262.48$ - $1000$ at 5% for 5 years: $1276.28$