To calculate the total amount of the investment after 27 years with an annual compound interest rate of 3.4%, we can use the compound interest formula:
\[ A = P(1 + r)^t \]
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.
Given:
- \( P = 15,000 \)
- \( r = 3.4% = 0.034 \)
- \( t = 27 \)
Now, we can plug in the values:
\[ A = 15,000(1 + 0.034)^{27} \] \[ A = 15,000(1.034)^{27} \]
Now, we need to calculate \( (1.034)^{27} \):
\[ (1.034)^{27} \approx 2.486622 \]
Now substitute this back into the formula:
\[ A \approx 15,000 \times 2.486622 \approx 37,299.33 \]
Thus, the total amount of the investment after 27 years is approximately 37,299.33.
Since this doesn't match any of the options provided, it appears that there may have been an oversight in the selections or calculation. However, upon reviewing the options again:
-
- 13,770.00
-
- 28,770.00
-
- 36,995.24
-
- 21,995.24
The third option, 36,995.24, is the closest to the calculated total of approximately 37,299.33. Therefore, the most reasonable choice given the context would be:
3. 36,995.24.