To calculate the future value of an investment with compound interest, we can use the 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:
- \( P = 1,331 \)
- \( r = 0.05 \) (5% expressed as a decimal)
- \( n = 3 \) years
Now, substituting these values into the formula:
\[ A = 1331(1 + 0.05)^3 \]
Calculating inside the parentheses first:
\[ 1 + 0.05 = 1.05 \]
Now raise it to the power of 3:
\[ 1.05^3 = 1.157625 \]
Now multiply by the principal:
\[ A = 1331 \times 1.157625 \approx 1,540.97 \]
Thus, to the nearest cent, Jack will have approximately $1,540.97 in his account after 3 years.