$1 \leftarrow \quad$ Use the compound interest formulas $\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{\mathrm{n}}\right)^{\mathrm{nt}}$ and $\mathrm{A}=\mathrm{P} e^{\mathrm{rt}}$ to solve the problem given. Round answers to the nearest cent. compounded continuously.
a. What is the accumulated value if the money is compounded semiannually?
(Round your answer to the nearest cent. Do not include the $\$$ symbol in your answer.)
Answer
Final Answer: The accumulated value if the money is compounded semiannually is \(\boxed{1280.08}\).
Step 1 ：Given the principal amount (P) as $1000, the annual interest rate (r) as 0.05, the time in years (t) as 5, and the number of times that interest is compounded per year (n) as 2.
Step 2 ：The formula for compound interest when compounded semiannually is \(A = P(1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.
Step 3 ：Substitute the given values into the formula: \(A = 1000(1 + \frac{0.05}{2})^{2*5}\)
Step 4 ：Calculate the value of A to get the accumulated value.
Step 5 ：Final Answer: The accumulated value if the money is compounded semiannually is \(\boxed{1280.08}\).
