Question

Brendan deposited $3,967 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will he 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 earned, we'll use the formula for compound interest:

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

where:
- \( B \) is the final balance,
- \( p \) is the principal (the initial amount),
- \( r \) is the interest rate (as a decimal),
- \( t \) is the time in years.

Given:
- \( p = 3967 \) (the initial deposit),
- \( r = 0.05 \) (the interest rate of 5% expressed as a decimal),
- \( t = 5 \) (the number of years).

Now, let's plug in the values into the formula:

\[
B = 3967(1 + 0.05)^5
\]

First, calculate \( 1 + 0.05 \):

\[
1 + 0.05 = 1.05
\]

Now raise \( 1.05 \) to the power of 5:

\[
1.05^5 \approx 1.2762815625
\]

Next, calculate \( B \):

\[
B = 3967 \times 1.2762815625 \approx 5067.15
\]

Now we can find the interest earned by subtracting the principal from the final balance:

\[
\text{Interest} = B - p = 5067.15 - 3967 = 1100.15
\]

To the nearest cent, the interest Brendan will earn in 5 years is:

\[
\boxed{1100.15}
\]