To calculate the maximum value of Briar's investment, we will use the formula for compound interest, assuming the interest is compounded annually:
\[ A = P(1 + r)^n \]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested.
Given:
- \( P = 7,800 \)
- \( r = 4.1% = 0.041 \)
- \( n = 3 \)
Now we can substitute these values into the compound interest formula:
\[ A = 7,800 \times (1 + 0.041)^3 \] \[ A = 7,800 \times (1.041)^3 \] \[ A = 7,800 \times 1.1277281 \quad (\text{approximating } (1.041)^3) \] \[ A \approx 8,806.08 \]
Now, rounding to the nearest hundred:
\[ \text{maximum value} \approx 8,800 \]
Therefore, the maximum value Briar can expect this investment to achieve is $8,800.
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