Question

Tony has $5,665 in an account that earns 6% interest compounded annually.
To the nearest cent, how much interest will he earn in 3 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.
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Answer 1

To find out how much interest Tony will earn in 3 years, we can use the formula you provided:

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

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

Given:
- \( p = 5665 \)
- \( r = 0.06 \) (6% as a decimal)
- \( t = 3 \)

Let's calculate the balance \( B \):

1. Substitute the values into the formula:

\[
B = 5665(1 + 0.06)^3
\]

2. Calculate \( 1 + 0.06 \):

\[
1 + 0.06 = 1.06
\]

3. Now raise \( 1.06 \) to the power of 3:

\[
1.06^3 \approx 1.191016
\]

4. Now multiply by the principal \( p \):

\[
B \approx 5665 \times 1.191016 \approx 6765.15
\]

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

\[
\text{Interest} = B - p = 6765.15 - 5665 = 1100.15
\]

To the nearest cent, the interest Tony will earn in 3 years is:

\[
\boxed{1100.15}
\]