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 answer

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.