Question 6 (2 points)
A student received $\$ 750$ in high school graduation gifts. The money is invested in a compound interest account, at an annual rate of $4 \%$, compounded semi-annually.
Use the compound interest formula in Unit 4 Chapter 3 and your calculator to answer the following questions (fill in the blank as directed).
How much money does the student have after 4 years? Round your answer to the nearest dollar.
A How long in years is required to double the
investment? Round your answer to the nearest tenth.
A What interest rate is need to double the money in 5 years? Express your answer to the nearest percent.
A
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Answer
Round this amount to the nearest dollar to get the final answer: \(\boxed{879}\) dollars.
Step 1 ：Given that the principal amount (P) is $750, the annual interest rate (r) is 4% or 0.04, the number of times interest is compounded per year (n) is 2, and the number of years (t) is 4.
Step 2 ：We can use the compound interest formula \(A = P(1 + \frac{r}{n})^{nt}\) to calculate the amount of money the student will have after 4 years.
Step 3 ：Substitute the given values into the formula: \(A = 750(1 + \frac{0.04}{2})^{2*4}\).
Step 4 ：Calculate the value inside the parentheses: \(1 + \frac{0.04}{2} = 1.02\).
Step 5 ：Raise 1.02 to the power of 8: \(1.02^{8} = 1.17186\).
Step 6 ：Multiply 750 by 1.17186 to get the total amount: \(750 * 1.17186 = 878.895\).
Step 7 ：Round this amount to the nearest dollar to get the final answer: \(\boxed{879}\) dollars.
