Question

Craig has $4,427 in an account. The interest rate is 2% 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, 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:
- \( P = 4427 \)
- \( r = 0.02 \) (2% as a decimal)
- \( n = 4 \)

Now we can plug in the values:

\[
A = 4427(1 + 0.02)^4
\]

Calculating \( (1 + 0.02)^4 \):

\[
(1.02)^4 = 1.08243216
\]

Now plug this back into the equation:

\[
A = 4427 \times 1.08243216
\]

Calculating \( A \):

\[
A \approx 4781.15
\]

Now, to find the interest earned in 4 years, we subtract the principal from this amount:

\[
\text{Interest} = A - P = 4781.15 - 4427 = 354.15
\]

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

\[
\boxed{354.15}
\]