mandy boullet needs $17,000 to prepare her we...
mandy boullet needs $17,000 to prepare her web - page design business for opening. her bank will loan her the money at a bankers discount rate of 11.4% for 233 days. find the face value of the note so that ms. boullet will have the required $17,000. use bankers interest of 360 days. the face value of the simple discount note is $ (round to the nearest cent.)
Answer
# Explanation:
## Step1: Recall the banker's discount formula
The formula for the proceeds $P$ of a simple - discount note is $P = F(1 - dt)$, where $P$ is the proceeds (the amount of money the borrower receives), $F$ is the face - value of the note, $d$ is the discount rate, and $t$ is the time in years. We know that $P=\$17000$, $d = 0.114$, and $t=\frac{233}{360}$. We need to solve for $F$.
## Step2: Rearrange the formula to solve for $F$
Starting with $P = F(1 - dt)$, we can rewrite it as $F=\frac{P}{1 - dt}$.
## Step3: Substitute the given values into the formula
Substitute $P = 17000$, $d = 0.114$, and $t=\frac{233}{360}$ into the formula:
\[
\begin{align*}
1 - dt&=1-0.114\times\frac{233}{360}\\
&=1-\frac{0.114\times233}{360}\\
&=1-\frac{26.562}{360}\\
&=1 - 0.0737833\\
&=0.9262167
\end{align*}
\]
Then $F=\frac{17000}{0.9262167}\approx18354.65$.
# Answer:
$18354.65$