Question

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sam and edna deposit $600.00 into a savings account which earns 4% 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.

Explanation:

Step1: Identify the formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years.

Step2: Convert the interest rate to decimal

The interest rate $r = 4\%=0.04$, $P=\$600$, and $t = 1$ year.

Step3: Substitute the values into the formula

$A=600\times e^{0.04\times1}$.

Step4: Calculate the value

Using a calculator, $e^{0.04}\approx1.04081077$, so $A = 600\times1.04081077\approx624.49$.

Answer:

$624.49$