mandy boullet needs $17,000 to prepare her web - page design business for opening. her bank will loan her…

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.)

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:

$18354.65$