Question

Tessa puts $8,000.00 into an account to use for school expenses. The account earns 7% interest, compounded continuously. How much will be in the account after 4 years?
Round your answer to the nearest cent.
$

Answer 1

To calculate the amount in the account after 4 years with continuous compounding interest, you can use the formula:

\[
A = Pe^{rt}
\]

where:
- \( A \) is the amount of money accumulated after time \( t \),
- \( P \) is the principal amount (the initial amount of money),
- \( r \) is the annual interest rate (decimal),
- \( t \) is the time the money is invested for (in years),
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

Given:
- \( P = 8000 \) (the initial amount),
- \( r = 0.07 \) (7% interest),
- \( t = 4 \) (4 years).

Substituting the values into the formula, we get:

\[
A = 8000 \times e^{0.07 \times 4}
\]

Calculating \( 0.07 \times 4 \):

\[
0.07 \times 4 = 0.28
\]

Now, we calculate \( e^{0.28} \):

\[
e^{0.28} \approx 1.32313
\]

Now substitute back into the formula:

\[
A \approx 8000 \times 1.32313
\]

Calculating \( 8000 \times 1.32313 \):

\[
A \approx 10585.04
\]

Rounding to the nearest cent:

\[
A \approx 10585.04
\]

Therefore, the amount in the account after 4 years will be **$10,585.04**.