Chandler Chen
10/03/2023 · High School

Suppose that \( \$ 59,000 \) is invested at \( 4 \frac{1}{2} \% \) 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 \( t=0,2,6 \), and 10 years. a) The function for the amount to which the investment grows after t years is \( \mathrm{A}(\mathrm{t})= \) (Simplify your answer. Type an expression using t as the variable.) b) Find the amount of money in the account at \( \mathrm{t}=0,2,6 \), and 10 years. The amount of money in the account at \( \mathrm{t}=0 \) years is \( \$ \square \). (Round to the nearest dollar as needed.) The amount of money in the account at \( \mathrm{t}=2 \) years is \( \$ \square \). (Round to the nearest dollar as needed.)

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a) \( A(t) = 59000 \left(1.01125\right)^{4t} \) b) At \( t=0 \): \( \$ 59000 \), At \( t=2 \): \( \$ 64524 \), At \( t=6 \): \( \$ 76664 \), At \( t=10 \): \( \$ 87823 \)

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