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! (1 point) Responses $13,770.00 $13,770.00 $28,770.00 $28,770.00 $36,995.24 $36,995.24 $21,995.24 $21,995.24

Answer 1

To find the total amount of Chris's investment after 27 years with an annual compound interest rate of 3.4%, we can use the compound interest formula:

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

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 or borrowed.

In this case:
- \(P = 15,000\)
- \(r = 3.4/100 = 0.034\)
- \(n = 27\)

Now we can substitute the values into the formula:

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

Calculating the value inside the parentheses first:

\[
1 + 0.034 = 1.034
\]

Next, we raise this to the power of 27:

\[
1.034^{27} \approx 2.479589
\]

Now we multiply this result by the principal amount:

\[
A = 15000 \times 2.479589 \approx 37193.84
\]

Rounding to the nearest cent, the total amount of the investment after 27 years is approximately:

\[
A \approx 37193.84
\]

From the provided options, the closest amount is **$36,995.24**. Thus, the rounded answer is:

**$36,995.24**.