Question

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



Compound Interest Formula:

Answer 1

To calculate the amount Jim will have after 10 years with continuous compounding, we can use the formula for continuously compounded interest:

\[
A = Pe^{rt}
\]

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 time the money is invested for in years.
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828).

In this case:
- \( P = 1526 \)
- \( r = 0.08 \) (which is 8% expressed as a decimal)
- \( t = 10 \)

Now we can substitute the values into the formula:

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

Calculating the exponent:

\[
0.08 \times 10 = 0.8
\]

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

\[
e^{0.8} \approx 2.22554 \text{ (using a calculator)}
\]

Now, substitute back into the formula:

\[
A = 1526 \times 2.22554 \approx 3395.54
\]

So, after 10 years, Jim will have approximately **$3395.54**.