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 interest Gabrielle will earn in 5 years, we can use the formula:

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

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

Now, let's plug in these values:

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

Calculating the expression inside the parentheses first:

\[
1 + 0.05 = 1.05.
\]

Now raise that to the power of 5:

\[
1.05^5.
\]

Calculating \( 1.05^5 \):

\[
1.05^5 \approx 1.2762815625.
\]

Now we can calculate \( B \):

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

Calculating that gives:

\[
B \approx 6381.4078125.
\]

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

\[
\text{Interest} = B - p = 6381.4078125 - 5000 = 1381.4078125.
\]

Rounding to the nearest cent, the interest Gabrielle will earn in 5 years is:

\[
\text{Interest} \approx \text{\$}1381.41.
\]

Thus, the final answer is:

\[
\boxed{1381.41}.
\]