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.