$900 are deposited in an account with 7% interest rate, compounded continuously. what is the balance after 6…

Explanation:

Step1: Identify the formula

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

Step2: Convert the interest rate to decimal

The interest rate $r = 7%=0.07$, $P = 900$, and $t = 6$.

Step3: Substitute the values into the formula

$A=900\times e^{0.07\times6}$.

Step4: Calculate the exponent

$0.07\times6 = 0.42$. So, $A = 900\times e^{0.42}$.

Step5: Evaluate $e^{0.42}$

Using a calculator, $e^{0.42}\approx1.52196$.

Step6: Calculate the final amount

$A = 900\times1.52196=1369.764\approx1369.76$.

Answer:

$1369.76$