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 Chris's investment after 27 years using the formula for compound interest, you can use the formula:

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

where:
- \( A \) is the total amount after time \( t \),
- \( P \) is the principal amount (initial investment),
- \( r \) is the annual interest rate (as a decimal),
- \( t \) is the number of years.

Given:
- \( P = 15,000 \) (the initial amount),
- \( r = 3.4\% = 0.034 \) (the annual interest rate in decimal),
- \( t = 27 \) (the number of years).

Now, plug in the values into the formula:

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

Calculating \( 1 + 0.034 \):

\[
1 + 0.034 = 1.034
\]

Now raise this to the power of 27:

\[
1.034^{27} \approx 2.463
\]

Now substitute back into the formula:

\[
A \approx 15000 \times 2.463
\]

Calculating the final amount:

\[
A \approx 36945.00
\]

Therefore, the total amount of the investment after 27 years is approximately **$36,945.00**.