Question

3600 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 25 years, to the nearest cent?

Answer 1

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:

\[
\boxed{31122.00}
\]