To calculate the future value of Atticus's investment, we can use the formula for compound interest:
\[ A = P(1 + r)^n \]
where:
- \(A\) is the amount of money accumulated after n years, including interest.
- \(P\) is the principal amount (initial investment).
- \(r\) is the annual interest rate (decimal).
- \(n\) is the number of years the money is invested for.
Given:
- \(P = 6400\)
- \(r = 3.2% = 0.032\)
- \(n = 6\)
Now, let's plug the values into the formula:
\[ A = 6400(1 + 0.032)^6 \] \[ A = 6400(1.032)^6 \]
Calculating \((1.032)^6\):
\[ 1.032^6 \approx 1.207135 \]
Now substitute that back into the equation for \(A\):
\[ A \approx 6400 \times 1.207135 \approx 7725.66 \]
Rounding to the nearest whole number, the expected maximum value of the investment is:
\[ \boxed{7726} \]
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