reggie and maya deposit $6,798.00 into a savings account which earns 14% interest compounded continuously…

reggie and maya deposit $6,798.00 into a savings account which earns 14% 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.

reggie and maya deposit $6,798.00 into a savings account which earns 14% 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 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 $r = 14%=0.14$, $P=$6798$, and $t = 1$ year.

Step3: Substitute the values into the formula

$A=6798\times e^{0.14\times1}=6798\times e^{0.14}$.

Step4: Calculate the value

Using a calculator, $e^{0.14}\approx1.150272$, then $A = 6798\times1.150272\approx7818.34$.

Answer:

$7818.34$