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 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:

\[ \boxed{36894.00} \]