To determine the future value of an investment, we can use the formula for compound interest. The formula is:
[tex]\[ FV = P \times (1 + r)^n \][/tex]
where:
- [tex]\(FV\)[/tex] is the future value of the investment,
- [tex]\(P\)[/tex] is the principal amount (initial investment),
- [tex]\(r\)[/tex] is the annual interest rate (as a decimal),
- [tex]\(n\)[/tex] is the number of years the money is invested.
Given the values:
- Principal ([tex]\(P\)[/tex]) = [tex]$600,
- Annual interest rate (\(r\)) = 11% = 0.11,
- Number of years (\(n\)) = 4,
we plug these values into the formula:
\[ FV = 600 \times (1 + 0.11)^4 \]
Calculating step-by-step:
1. Add 1 to the interest rate:
\[ 1 + 0.11 = 1.11 \]
2. Raise 1.11 to the power of 4 (since the investment is for four years):
\[ 1.11^4 = 1.11 \times 1.11 \times 1.11 \times 1.11 \]
3. Multiply the principal by this value:
\[ 600 \times 1.11^4 = 600 \times 1.534615 \approx 910.84 \]
Therefore, the future value of the $[/tex]600 investment after four years at an annual interest rate of 11% is approximately:
[tex]\[ FV \approx \$910.84 \][/tex]
So, the correct answer is:
O
$910.84
