Question

Chris invests $15,000 in a retirement account with an annual compound interest rate of 3.4%. Find the total amount of the investment after 27 years. Round answers to the nearest cent (hundredth). *Remember to use your STAAR Reference Sheet for support! (

Answer 1

To calculate the total amount of money in a retirement account after a certain number of years with compound interest, you can use the formula:

\[
A = P(1 + r)^t
\]

Where:
- \(A\) = the amount of money accumulated after n years, including interest.
- \(P\) = the principal amount (the initial amount of money).
- \(r\) = the annual interest rate (decimal).
- \(t\) = the number of years the money is invested or borrowed.

In this case:
- \(P = 15000\)
- \(r = 3.4\% = 0.034\)
- \(t = 27\) years

Plugging in the values:

\[
A = 15000(1 + 0.034)^{27}
\]

\[
A = 15000(1.034)^{27}
\]

Now, we will calculate \( (1.034)^{27} \):

\[
(1.034)^{27} \approx 2.4596 \quad (\text{using a calculator})
\]

Now, we will multiply this value by 15,000:

\[
A = 15000 \times 2.4596 \approx 36894.00
\]

Thus, the total amount of the investment after 27 years is approximately \(\$36,894.00\).

Rounded to the nearest cent, the final amount in Chris's retirement account after 27 years is:

\[
\boxed{36894.00}
\]