Question

Derek deposited $7,000 in an account earning 15% 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

Answer 1

To calculate the balance \( B \) using the formula \( B = p(1 + r)^t \), we need to identify the values for \( p \), \( r \), and \( t \):

- \( p = 7000 \) (the principal)
- \( r = 0.15 \) (the interest rate expressed as a decimal, since 15% = 0.15)
- \( t = 3 \) (the time in years)

Now, we can substitute these values into the formula:

\[
B = 7000 \times (1 + 0.15)^3
\]

First, calculate \( (1 + 0.15) \):

\[
1 + 0.15 = 1.15
\]

Next, calculate \( (1.15)^3 \):

\[
(1.15)^3 = 1.15 \times 1.15 \times 1.15 \approx 1.520875
\]

Now, substitute this value back into the formula for \( B \):

\[
B = 7000 \times 1.520875
\]

Calculating this gives:

\[
B \approx 10645.125
\]

To find the interest earned, we subtract the principal from the balance:

\[
\text{Interest} = B - p = 10645.125 - 7000 = 3645.125
\]

Rounding to the nearest cent:

\[
\text{Interest} \approx 3645.13
\]

Thus, the interest Derek will earn in 3 years is approximately **$3645.13**.