pablo and sidney deposit $3,000.00 into a savings account which earns 6% interest compounded continuously…

pablo and sidney deposit $3,000.00 into a savings account which earns 6% 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.

pablo and sidney deposit $3,000.00 into a savings account which earns 6% 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

Explanation:

Step1: Identify the continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the percentage to decimal

The annual interest rate $r = 6%=0.06$, the principal amount $P=$3000$, and the time $t = 1$ year.

Step3: Substitute the values into the formula

Substitute $P = 3000$, $r=0.06$, and $t = 1$ into the formula $A = Pe^{rt}$. We get $A=3000\times e^{0.06\times1}$.

Step4: Calculate the value of $A$

Using a calculator, $e^{0.06}\approx1.0618365465$. Then $A = 3000\times1.0618365465\approx3185.51$.

Answer:

$3185.51$