1. **State the problem:** Alayna invested 3916 with an interest rate of 3% compounded 12 times a year for 3 years. We need to find the total value of her investment now. 2. **Formula used:** The formula for compound interest is: $$A = P \left(1 + \frac{r}{n}\right)^{nt}$$ where: - $A$ is the amount of money accumulated after $t$ years, including interest. - $P$ is the principal amount (initial investment). - $r$ is the annual interest rate (decimal). - $n$ is the number of times interest is compounded per year. - $t$ is the time the money is invested for in years. 3. **Identify values:** - $P = 3916$ - $r = 0.03$ (3% as a decimal) - $n = 12$ - $t = 3$ 4. **Substitute values into the formula:** $$A = 3916 \left(1 + \frac{0.03}{12}\right)^{12 \times 3}$$ 5. **Simplify inside the parentheses:** $$1 + \frac{0.03}{12} = 1 + 0.0025 = 1.0025$$ 6. **Calculate the exponent:** $$12 \times 3 = 36$$ 7. **Calculate the total amount:** $$A = 3916 \times 1.0025^{36}$$ 8. **Calculate $1.0025^{36}$:** $$1.0025^{36} \approx 1.093443$$ 9. **Multiply to find $A$:** $$A = 3916 \times 1.093443 \approx 4282.88$$ **Final answer:** Alayna's investment is now worth approximately **4282.88**.