blake invested $66,000 in an account paying an interest rate of 5.7% compounded continuously. assuming no…

Explanation:

Step1: Recall 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 investment), $r$ is the annual interest rate (in decimal form), and $t$ is the number of years.

Step2: Convert the interest rate to decimal form

Given $r = 5.7%=0.057$, $P = 66000$, and $t = 20$.

Step3: Substitute the values into the formula

$A=66000\times e^{0.057\times20}$. First, calculate the exponent: $0.057\times20 = 1.14$. Then, find the value of $e^{1.14}$. Using a calculator, $e^{1.14}\approx3.126767$. Now, $A = 66000\times3.126767$. $A=206366.622$.

Step4: Round to the nearest hundred dollars

Rounding $206366.622$ to the nearest hundred dollars gives $206400$.

Answer:

$206400$