Question

Ed and Hayley deposit $700.00 into a savings account which earns 7% interest compounded continuously. They want to use the money in the account to go on a trip in 1 year. How much will they be able to spend?
Round your answer to the nearest cent.

Answer 1

To calculate the amount Ed and Hayley will have in their savings account after 1 year with continuous compounding, we can use the formula for continuous compound interest, which is:

\[
A = Pe^{rt}
\]

Where:
- \(A\) is the amount of money accumulated after time \(t\),
- \(P\) is the principal amount (the initial amount of money),
- \(r\) is the annual interest rate (in 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).

Given:
- \(P = 700\) (the initial deposit)
- \(r = 0.07\) (7% interest rate)
- \(t = 1\) (time in years)

Now we plug in the values:

\[
A = 700 \times e^{0.07 \times 1}
\]

First, we calculate \(e^{0.07}\):

Using a calculator, \(e^{0.07} \approx 1.072508\).

Now we can calculate \(A\):

\[
A \approx 700 \times 1.072508 \approx 750.756
\]

Rounding to the nearest cent:

\[
A \approx 750.76
\]

Thus, Ed and Hayley will have approximately **$750.76** to spend on their trip.