Investment Final Amount 4A01C0

1. **State the problem:** Calculate the final amount of an investment of €24,750 after 3 years with an Annual Equivalent Rate (AER) of 3.1%. 2. **Formula used:** The formula for compound interest using AER is $$A = P(1 + r)^t$$ where: - $A$ is the final amount - $P$ is the principal (initial investment) - $r$ is the annual interest rate (as a decimal) - $t$ is the time in years 3. **Convert the given values:** - $P = 24750$ - $r = 3.1\% = \frac{3.1}{100} = 0.031$ - $t = 3$ years 4. **Calculate the final amount:** $$A = 24750(1 + 0.031)^3$$ $$A = 24750(1.031)^3$$ 5. **Calculate the power:** $$1.031^3 = 1.031 \times 1.031 \times 1.031 = 1.095927$$ 6. **Multiply by the principal:** $$A = 24750 \times 1.095927 = 27115.07$$ 7. **Final answer:** The final amount after 3 years is **27115.07** (rounded to two decimal places).