owen is going to invest in an account paying an interest rate of 5.7% compounded continuously. how much…

Explanation:

Step1: Recall continuous - compounding formula

The formula for continuous - compounding is $A = Pe^{rt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We are given that $A=$122000$, $r = 0.057$ (since $5.7%=0.057$), and $t = 14$ years. We need to solve for $P$. From $A = Pe^{rt}$, we can rewrite it as $P=\frac{A}{e^{rt}}$.

Step2: Substitute the given values

Substitute $A = 122000$, $r=0.057$, and $t = 14$ into the formula $P=\frac{A}{e^{rt}}$. $P=\frac{122000}{e^{0.057\times14}}$. First, calculate the exponent: $0.057\times14 = 0.798$. Then, find $e^{0.798}$. Using a calculator, $e^{0.798}\approx2.2207$. So, $P=\frac{122000}{2.2207}\approx54937.5$.

Step3: Round to the nearest hundred dollars

Rounding $54937.5$ to the nearest hundred dollars gives $54900$.

Answer:

$54900$