To calculate the expected maximum value of the investment using the compound interest formula, we use:
\[ A = P(1 + r)^t \]
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).
- \( t \) is the number of years the money is invested or borrowed.
In this case:
- \( P = 9,400 \)
- \( r = 6.2% = 0.062 \)
- \( t = 7 \)
Now we can plug in the values:
\[ A = 9400(1 + 0.062)^7 \]
Calculating \( (1 + 0.062)^7 \):
\[ 1 + 0.062 = 1.062 \] \[ (1.062)^7 \approx 1.484812 \]
Now we calculate \( A \):
\[ A \approx 9400 \times 1.484812 \approx 13935.6308 \]
Rounding to the nearest hundred:
\[ A \approx 13900 \]
Therefore, the expected maximum value of the investment is:
\[ \text{Expected value} = $13,900 \]