Part 2 of 4 Points: 0.25 Use the compound interest formulas \( A=P\left(1+\frac{r}{n}\right)^{n t} \) and \( A=P e^{r t} \) to solve the problem given. Round answers to the Find the accumulated value of an investment of \( \$ 25,000 \) for 6 years at an interest rate of \( 4 \% \) if the money is a. compo compounded monthly; d. compounded continuously. a. What is the accumulated value if the money is compounded semiannually? \$31,706.04 (Round your answer to the nearest cent. Do not include the \$ symbol in your answer.) b. What is the accumulated value if the money is compounded quarterly? \$ \( \square \) (Round your answer to the nearest cent. Do not include the \( \$ \) symbol in your answer.)

To find the accumulated value for compound interest, we can use the formula \( A = P\left(1+\frac{r}{n}\right)^{nt} \). Given: - Principal \( P = 25,000 \) - Rate \( r = 0.04 \) - Time \( t = 6 \) years. **a. Compounded semiannually:** Here, \( n = 2 \) (compounded semiannually). \[ A = 25000\left(1+\frac{0.04}{2}\right)^{2 \times 6} \] \[ A = 25000\left(1+0.02\right)^{12} \] \[ A = 25000 \times (1.02)^{12} \] \[ A \approx 25000 \times 1.2682418 \approx 31670.04 \] So, the accumulated value if the money is compounded semiannually is **31,670.04**. **b. Compounded quarterly:** Here, \( n = 4 \) (compounded quarterly). \[ A = 25000\left(1+\frac{0.04}{4}\right)^{4 \times 6} \] \[ A = 25000\left(1+0.01\right)^{24} \] \[ A = 25000 \times (1.01)^{24} \] \[ A \approx 25000 \times 1.2682418 \approx 31670.04 \] So, the accumulated value if the money is compounded quarterly is **31,706.04**.