Question

$15,000 is invested at a rate of 8% compounded quarterly. Identify the compound interest function to model the situation. Then find the balance after 10 years. A = 15000(1.4)2t ; $31,044.81B = 15000(1.04)2t ; $32,866.85C = 15000(1.02)4t ; $33,120.59D = 15000(1.02)4t ; $30,582.44

Answer 1

The compound interest function to model the situation is B = 15000(1.02)4t. The balance after 10 years is approximately $33,120.59.

Step-by-step explanation:

The compound interest function to model the situation is B = 15000(1.02)4t. We use this function because the investment is compounded quarterly at a rate of 8% per year, which translates to a quarterly interest rate of 2%.

To find the balance after 10 years, we substitute t = 10 into the function and calculate: B = 15000(1.02)4(10)

Simplifying the expression, we get B = 15000(1.02)^40, which is approximately $33,120.59. Therefore, the correct answer is C.

Answer 2

`\begin{gathered} Compound\text{ interest: }A\text{ = \lparen1+i\%\rparen}^n \\ A\text{ = \lparen1+}(0.08)/(4))^(4t) \\ When\text{ t = 10} \\ A=\text{ 15000\lparen1.02\rparen}^(4(10)) \\ \text{ = 33120.59} \end{gathered}`

Correct option C