Compound Interest 2C9Add

1. **State the problem:** You borrow $2000 for three years at an annual compound interest rate of 12%. We need to find the total interest to be paid back after 3 years. 2. **Formula for compound interest:** The amount $A$ after $t$ years with principal $P$, annual interest rate $r$, compounded yearly is: $$A = P \times (1 + r)^t$$ where $r$ is in decimal form. 3. **Identify values:** - Principal $P = 2000$ - Rate $r = 12\% = 0.12$ - Time $t = 3$ years 4. **Calculate the amount:** $$A = 2000 \times (1 + 0.12)^3 = 2000 \times (1.12)^3$$ 5. **Calculate $(1.12)^3$ step-by-step:** $$1.12^2 = 1.12 \times 1.12 = 1.2544$$ $$1.12^3 = 1.2544 \times 1.12 = 1.404928$$ 6. **Calculate total amount:** $$A = 2000 \times 1.404928 = 2809.856$$ 7. **Calculate total interest:** Total interest $I = A - P = 2809.856 - 2000 = 809.856$ 8. **Final answer:** The total interest to be paid back after 3 years is approximately $809.86$.