Question

Celine has $997 in an account. The interest rate is 9% 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 find out how much interest Celine will earn in 2 years, we can use the formula \( B = p(1 + r)^t \).

Here are the values we have:
- \( p = 997 \) (the principal amount)
- \( r = 0.09 \) (the interest rate as a decimal)
- \( t = 2 \) (the time in years)

Now, we will substitute the values into the formula:

\[
B = 997(1 + 0.09)^2
\]

Calculating \( (1 + 0.09)^2 \):

\[
1 + 0.09 = 1.09
\]
\[
(1.09)^2 = 1.1881
\]

Now plug this back into the equation for \( B \):

\[
B = 997 \times 1.1881
\]
\[
B \approx 1189.67
\]

Now we will calculate the interest earned after 2 years by subtracting the principal from the final balance:

\[
\text{Interest} = B - p = 1189.67 - 997 = 192.67
\]

Thus, the amount of interest Celine will earn in 2 years, rounded to the nearest cent, is:

\[
\boxed{192.67}
\]