Question

rafi and kayla deposit $1,000.00 into a savings account which earns 1% 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. $ submit

Explanation:

Step1: Recall continuous compounding formula

The formula for continuous compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal), $t$ is the time in years, and $e$ is the base of the natural logarithm.
Here, $P = 1000$, $r = 0.01$ (since 1% = 0.01), and $t = 1$.

Step2: Substitute values into the formula

Substitute $P = 1000$, $r = 0.01$, and $t = 1$ into $A = Pe^{rt}$:
$A = 1000 \times e^{0.01 \times 1}$
$A = 1000 \times e^{0.01}$

Step3: Calculate the value of $e^{0.01}$ and then $A$

We know that $e^{0.01}\approx1.010050167$.
So, $A = 1000 \times 1.010050167 \approx 1010.05$

Answer:

$\$1010.05$