Question

Lamar deposited $9,651 in an account earning 10% interest compounded annually.
To the nearest cent, how much interest will he earn in 4 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 total amount \( B \) in the account after 4 years using the formula \( B = p(1 + r)^t \), we can plug in the values.

- \( p = 9,651 \) (the principal)
- \( r = 0.10 \) (the interest rate as a decimal)
- \( t = 4 \) (the time in years)

Now, substituting the values into the formula:

\[
B = 9,651(1 + 0.10)^4
\]

Calculating \( 1 + 0.10 \):

\[
1 + 0.10 = 1.10
\]

Now we raise \( 1.10 \) to the power of 4:

\[
(1.10)^4 = 1.4641
\]

Now we can multiply to find \( B \):

\[
B = 9,651 \times 1.4641
\]
\[
B \approx 14,168.2821
\]

Now, we can round this to the nearest cent:

\[
B \approx 14,168.28
\]

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

\[
\text{Interest} = B - p = 14,168.28 - 9,651 = 4,517.28
\]

Thus, to the nearest cent, the interest Lamar will earn in 4 years is:

\[
\boxed{4,517.28}
\]