Hardy Knight
02/03/2024 · High School

Suppose that \( \$ 88,000 \) is invested at \( 3 \frac{1}{2} \% \) interest, compounded quarterly. a) Find the function for the amount to which the investment grows after \( t \) years. b) Find the amount of money in the account at \( t=0,3,5 \), and 10 years. a) The function for the amount to which the investment grows after \( t \) years is \( A(t)=88000(1.00875)^{4 t} \). (Simplify your answer. Type an expression using \( t \) as the variable.) b) Find the amount of money in the account at \( t=0,3,5 \), and 10 years. The amount of money in the account at \( t=0 \) years is \( \$ 88,000 \). (Round to the nearest dollar as needed.) The amount of money in the account at \( t=3 \) years is \( \$ 97,698 \). (Round to the nearest dollar as needed.) The amount of money in the account at \( t=5 \) years is \( \$ \square \). (Round to the nearest dollar as needed.)

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a) The function for the amount to which the investment grows after \( t \) years is \( A(t)=88000(1.00875)^{4t} \). b) The amounts in the account are: - At \( t = 0 \): \( \$ 88,000 \) - At \( t = 3 \): \( \$ 97,430 \) - At \( t = 5 \): \( \$ 108,054 \) - At \( t = 10 \): \( \$ 130,458 \)

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