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 Skip to navigation

1 answer

To calculate the total amount of the investment after 27 years with an annual compound interest rate of 3.4%, we can use the formula for compound interest:

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

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).
  • \(t\) is the time the money is invested for, in years.

In this case:

  • \(P = 15,000\)
  • \(r = 3.4% = 0.034\)
  • \(t = 27\)

Plugging these values into the formula, we get:

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

Calculating \(1 + 0.034\):

\[ 1 + 0.034 = 1.034 \]

Now raise \(1.034\) to the power of \(27\):

\[ 1.034^{27} \approx 2.487610 \]

Now, multiply this by the principal amount:

\[ A \approx 15000 \times 2.487610 \approx 37314.15 \]

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

\[ A \approx 37314.15 \]

Thus, the options provided do not include this result, suggesting a verification or adjustment is necessary in choices provided or potentially in the interest calculation. However, the calculated value is approximately $37,314.15.

Always ensure to verify source data and recheck calculations or available choices. Consider confirming with financial growth calculators or further clarify options provided.