Question

Annie has $9,000 in an account that earns 5% interest compounded annually.
To the nearest cent, how much interest will she earn in 2 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 Annie will earn in 2 years on her $9,000 account with an interest rate of 5% compounded annually, we can use the formula:

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

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

Given:
- \( p = 9000 \)
- \( r = 0.05 \) (5% expressed as a decimal)
- \( t = 2 \)

Let's plug in the values:

\[
B = 9000(1 + 0.05)^2
\]

Calculating this step by step:

1. Calculate \( (1 + 0.05) \):
\[
1 + 0.05 = 1.05
\]

2. Raise \( 1.05 \) to the power of \( 2 \):
\[
(1.05)^2 = 1.1025
\]

3. Multiply \( 9000 \) by \( 1.1025 \):
\[
B = 9000 \times 1.1025 = 9912.5
\]

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

\[
\text{Interest} = B - p = 9912.5 - 9000 = 912.5
\]

To the nearest cent, the interest Annie will earn in 2 years is:

\[
\boxed{912.50}
\]