Questions: Find the amount that results from the given investment. 600 invested at 11% compounded quarterly after a period of 2 years After 2 years, the investment results in . (Round to the nearest cent as needed.)

Find the amount that results from the given investment. 600 invested at 11% compounded quarterly after a period of 2 years After 2 years, the investment results in . (Round to the nearest cent as needed.)
Transcript text: Find the amount that results from the given investment. $\$ 600$ invested at $11 \%$ compounded quarterly after a period of 2 years After 2 years, the investment results in \$ $\square$ . (Round to the nearest cent as needed.)
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Solution

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Solution Steps

Step 1: Convert the Annual Interest Rate to a Decimal

The annual interest rate is given as 11%. To convert it to a decimal, we divide by 100: \[r = \frac{11}{100} = 0.11\]

Step 2: Identify the Number of Times the Interest is Compounded Per Year

The interest is compounded 4 times per year.

Step 3: Calculate the Future Value Using the Compound Interest Formula

The compound interest formula is given by: \[A = P \left(1 + \frac{r}{n}\right)^{nt}\] Plugging in the values, we get: \[A = 600 \left(1 + \frac{0.11}{4}\right)^{4*2} = 745.43\]

Final Answer:

The future value of the investment, rounded to 2 decimal places, is $745.43.

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