Question

Suzie has $9,126 in an account. The interest rate is 10% compounded annually.
To the nearest cent, how much interest will she earn in 5 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 earned over 5 years using the formula \( B = p(1 + r)^t \), we will substitute the values:

- \( p = 9126 \) (the principal or starting amount)
- \( r = 0.10 \) (the interest rate expressed as a decimal)
- \( t = 5 \) (the time in years)

Using the formula:

\[
B = 9126(1 + 0.10)^5
\]

First, calculate \( (1 + 0.10)^5 \):

\[
1.10^5 = 1.61051 \quad (\text{approximately})
\]

Now, use this value in the formula to find \( B \):

\[
B = 9126 \times 1.61051
\]

Calculating \( B \):

\[
B \approx 14765.35
\]

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

\[
\text{Interest} = B - p = 14765.35 - 9126
\]

Calculating the interest:

\[
\text{Interest} \approx 5639.35
\]

Thus, the interest earned in 5 years is approximately:

\[
\boxed{5639.35}
\]