Question

Debbie has $4,000 in an account. The interest rate is 15% 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.
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Answer 1

To calculate the interest Debbie will earn in 2 years, we use the formula:

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

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

Given:
- \(p = 4000\)
- \(r = 15\% = 0.15\)
- \(t = 2\)

Now we can substitute the values into the formula:

\[
B = 4000(1 + 0.15)^2
\]

Calculating \(1 + 0.15\):

\[
1 + 0.15 = 1.15
\]

Now, raise \(1.15\) to the power of 2:

\[
1.15^2 = 1.3225
\]

Now we will substitute back into the equation for \(B\):

\[
B = 4000 \times 1.3225 = 5290
\]

So, the final amount \(B\) after 2 years is \(5290\) dollars.

To find the interest earned, we subtract the principal from the final amount:

\[
\text{Interest} = B - p = 5290 - 4000 = 1290
\]

Thus, the amount of interest Debbie will earn in 2 years is \(\$1290.00\).