Question

Jeffrey puts $800.00 into an account to use for school expenses. The account earns 8% interest, compounded continuously. How much will be in the account after 10 years?
Round your answer to the nearest cent.
$

Answer 1

To calculate the amount in the account after 10 years with continuous compounding interest, we can use the formula for continuous compounding:

\[
A = Pe^{rt}
\]

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

Given:
- \(P = 800.00\),
- \(r = 0.08\) (8% as a decimal),
- \(t = 10\).

Now, we can substitute these values into the formula:

\[
A = 800 \times e^{(0.08 \times 10)}
\]

Calculate the exponent:

\[
0.08 \times 10 = 0.8
\]

Now calculate \(e^{0.8}\):

\[
A = 800 \times e^{0.8} \approx 800 \times 2.22554 \quad (\text{using } e^{0.8} \approx 2.22554)
\]

Now we multiply:

\[
A \approx 800 \times 2.22554 \approx 1780.43
\]

Therefore, rounding to the nearest cent:

\[
\boxed{1780.43}
\]

So, the amount in the account after 10 years will be approximately $1780.43.