Question

Jada is saving up money to buy a car. Jada puts $5,000.00 into an account which earns 6% interest, compounded continuously. How much will she have in the account after 1 year?
Round your answer to the nearest cent.
$

Answer 1

To calculate the amount Jada will have in her account after 1 year with continuously compounded interest, we can use the formula for continuous compounding:

\[
A = Pe^{rt}
\]

Where:
- \(A\) is the amount of money accumulated after time \(t\)
- \(P\) is the principal amount (initial investment)
- \(r\) 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)

In this case:
- \(P = 5000\)
- \(r = 0.06\)
- \(t = 1\)

Now we can plug the values into the formula:

\[
A = 5000 \cdot e^{0.06 \cdot 1}
\]

First, we calculate \(0.06 \cdot 1\):

\[
0.06 \cdot 1 = 0.06
\]

Next, we find \(e^{0.06}\):

\[
e^{0.06} \approx 1.061837
\]

Now we can calculate \(A\):

\[
A = 5000 \cdot 1.061837
\]

\[
A \approx 5309.185
\]

Rounding to the nearest cent, Jada will have approximately:

\[
A \approx 5309.19
\]

Thus, after 1 year, Jada will have **$5,309.19** in the account.