Question

Gabrielle deposited $5,000 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 5 years?
Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.

Answer 1

To calculate the future balance and the interest earned, we can use the formula:

\[
B = p(1 + r)^t
\]

where:
- \( p = 5000 \) (the principal amount),
- \( r = 0.05 \) (the interest rate as a decimal),
- \( t = 5 \) (the time in years).

Plugging in the values:

\[
B = 5000(1 + 0.05)^5
\]

Calculating \( (1 + 0.05)^5 \):

\[
(1.05)^5 \approx 1.2762815625
\]

Now we calculate \( B \):

\[
B \approx 5000 \times 1.2762815625 \approx 6381.4078125
\]

Now, to find the interest earned, we subtract the principal from the balance:

\[
\text{Interest} = B - p = 6381.41 - 5000 \approx 1381.41
\]

Thus, the interest earned to the nearest cent is:

\[
\boxed{1381.41}
\]