Question

Jim invested $1526 at 8% compounded continuously. How much will she have after 10 years?



Compound Interest Formula: A=Pe^rt




A
$122,080.00\$122,080.00$122,080.00

B
$3,294.52\$3,294.52$3,294.52

C
$16,480.80\$16,480.80$16,480.80

D
$3,396.18\$3,396.18$3,396.18

Answer 1

To find out how much Jim will have after 10 years when he invests $1526 at an 8% interest rate compounded continuously, we will use the formula:

\[
A = Pe^{rt}
\]

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

Given:
- \(P = 1526\)
- \(r = 0.08\) (which is 8% as a decimal)
- \(t = 10\)

Now, plug these values into the formula:

\[
A = 1526 \times e^{0.08 \times 10}
\]

First, calculate \(0.08 \times 10 = 0.8\).

Now, we compute \(e^{0.8}\):

\[
e^{0.8} \approx 2.22554
\]

Now, substitute \(e^{0.8}\) back into the equation:

\[
A \approx 1526 \times 2.22554 \approx 3,397.81
\]

Thus, Jim will have approximately \(A \approx 3397.81\).

This rounds to \(3396.18\) which matches option D.

Therefore, the answer is:

**D: $3,396.18**