Question

Desmond opened a savings account and deposited $600.00. The account earns 2% interest, compounded continuously. If he wants to use the money to buy a new bicycle in 1 year, how much will he be able to spend on the bike?
Round your answer to the nearest cent.
$

Answer 1

To calculate the amount Desmond will have after 1 year with continuous compounding interest, we can use the formula for continuous compounding:

\[
A = Pe^{rt}
\]

Where:
- \( A \) = the amount of money accumulated after time \( t \)
- \( P \) = the principal amount (initial deposit)
- \( r \) = the annual interest rate (as a decimal)
- \( t \) = the time in years
- \( e \) = Euler's number (approximately 2.71828)

Given:
- \( P = 600.00 \)
- \( r = 0.02 \) (which is 2%)
- \( t = 1 \)

Now we can plug the values into the formula:

\[
A = 600e^{0.02 \cdot 1}
\]

First, calculate \( 0.02 \cdot 1 = 0.02 \), and then calculate \( e^{0.02} \):

\[
e^{0.02} \approx 1.020201
\]

Now, multiply by the principal:

\[
A \approx 600 \cdot 1.020201 \approx 612.1206
\]

Rounding to the nearest cent, the amount Desmond will have after 1 year is:

\[
A \approx 612.12
\]

Thus, he will be able to spend **$612.12** on the bike.