To calculate the future value of a savings account with compound interest, you 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:
- \(P = 3000\)
- \(r = 0.03\) (3% expressed as a decimal)
- \(n = 5\)
Now, plug the values into the formula:
\[ A = 3000(1 + 0.03)^5 \]
First, calculate \(1 + 0.03\):
\[ 1 + 0.03 = 1.03 \]
Now raise \(1.03\) to the power of 5:
\[ 1.03^5 \approx 1.159274 \]
Next, multiply this by the principal \(P\):
\[ A = 3000 \times 1.159274 \approx 3477.82 \]
Finally, rounding to two decimal places, the value after five years will be:
\[ \boxed{3477.82} \]