Question

Clayton deposited $1,132 in an account earning 12% interest compounded annually.
To the nearest cent, how much will he have 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 balance \( B \) after 5 years using the formula \( B = p(1 + r)^t \), we first need to identify the values of \( p \), \( r \), and \( t \):

- \( p = 1,132 \)
- \( r = 12\% = 0.12 \) (expressed as a decimal)
- \( t = 5 \)

Now we can substitute these values into the formula:

\[
B = 1132(1 + 0.12)^5
\]

First, calculate \( (1 + 0.12) \):

\[
1 + 0.12 = 1.12
\]

Next, raise \( 1.12 \) to the power of 5:

\[
1.12^5 \approx 1.76234
\]

Now, multiply this value by the principal \( 1132 \):

\[
B \approx 1132 \times 1.76234 \approx 1990.05
\]

To the nearest cent, Clayton will have approximately:

\[
\boxed{1990.05}
\]

This means Clayton will have $1,990.05 in his account after 5 years.