Question

Find the value after five years of a $3,000 savings account that pays 3% interest compounded yearly. Round the answer to two decimal places

Answer 1

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:

\[
\boxed{3477.82}
\]