To find out how much money will be in the account after 25 years with an initial amount of \( P = 3600 \) and an annual interest rate of \( r = 0.09 \), we can use the formula for compound interest, which is:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the amount in the account after \( t \) years,
- \( P \) 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.
For this scenario, \( t = 25 \).
Substituting the values into the formula:
\[ A = 3600(1 + 0.09)^{25} \]
Calculating \( 1 + 0.09 \):
\[ 1 + 0.09 = 1.09 \]
Now substituting that back into the formula:
\[ A = 3600(1.09)^{25} \]
Next, we will calculate \( (1.09)^{25} \):
Using a calculator, we find that:
\[ (1.09)^{25} \approx 8.645 \]
Now we substitute that value back in to find \( A \):
\[ A \approx 3600 \times 8.645 \approx 31122 \]
Finally, rounding it to the nearest cent does not apply here as it is a whole number. So, the amount in the account after 25 years is approximately:
\[ \boxed{31122.00} \]
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