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.