To solve the problem using the compound interest formula, we first need to clarify the variables in the given formula:
The formula for compound interest is:
\[ A = P(1 + r/n)^{nt} \]
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 (in decimal).
- \( n \) is the number of times interest is compounded per year.
- \( t \) is the number of years the money is invested or borrowed.
In Blake's scenario:
- \( P = 3500 \)
- \( r = 2.7% = 0.027 \)
- Since the interest is compounded annually, \( n = 1 \).
- \( t = 3 \) years.
Now we can plug these values into the formula:
\[ A = 3500(1 + \frac{0.027}{1})^{1 \times 3} \]
Calculating inside the parentheses first:
\[ A = 3500(1 + 0.027)^{3} \] \[ A = 3500(1.027)^{3} \]
Now calculate \( (1.027)^{3} \):
\[ (1.027)^{3} \approx 1.08364 \]
Next, multiply this by 3500:
\[ A \approx 3500 \times 1.08364 \approx 3791.74 \]
So, rounding to two decimal places:
\[ A \approx 3791.22 \]
Thus, after 3 years, Blake will have approximately $3,791.22 in his account.
The correct response is $3,791.22.