Question

Albert has $1,000 in an account. The interest rate is 5% compounded annually.
To the nearest cent, how much interest will he earn in 4 years?
$

Answer 1

To calculate the interest earned on an account with compound interest, you can use the formula for compound interest:

\[
A = P(1 + r)^t
\]

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 or borrowed for, in years.

In this case:
- \( P = 1000 \)
- \( r = 0.05 \)
- \( t = 4 \)

Now, plug in the values:

\[
A = 1000(1 + 0.05)^4
\]

Calculating the expression inside the parentheses:

\[
1 + 0.05 = 1.05
\]

Now raise it to the power of 4:

\[
1.05^4 \approx 1.21550625
\]

Now multiply by the principal:

\[
A = 1000 \times 1.21550625 \approx 1215.51
\]

So, the total amount in the account after 4 years will be approximately $1215.51.

To find the interest earned, subtract the principal from the total amount:

\[
\text{Interest} = A - P = 1215.51 - 1000 = 215.51
\]

Thus, the interest earned in 4 years, to the nearest cent, is:

\[
\boxed{215.51}
\]