Question

You have saved $2500 for school this semester. Although you had hoped that this savings would cover all of your school expenses, you know that in all likelihood you will need to incur a student loan to cover expenses that exceed what you have saved. If you do incur a student loan, the money you receive from the loan will be reduced by a 1.5% origination fee charged by the lender. Complete the model to calculate the loan amount that you will need to incur to cover all of your school expenses including the loan fee.

Answer 1

Answer:

$z=1.0152x - 2538.07$

where $x$ is the total expenses and $z$ is the required loan needed to incur to cover all school expenses including the loan fee.

Explanation:

If total expenses is $x$, required loan is $z$ and loan charge is $y$, we can deduce the following relationship from the given: there is already a savings of $2500, therefore, the total expenses must be at least equal to savings plus loan minus loan charge i.e.

$x=2500+(z-y)$..........................................eq(1)  

but

$y=1.5% of z$% of $z$

$y=0.015z$..............................................eq(2)

substituting $y$ in eq(2) into eq(1), we have

$x=2500+(z-0.0152z)\\x=2500+0.985z$

rearranging,

$z=\frac{x-2500}{0.985}$$=1.0152x-2538.07$

∵$z=1.0152x-2538.07$..........................(3)

For example: suppose the total expenses $x$ is $4000, the required loan $z$ will be calculated as follows-

Applying equation 3,

$z=1.0152*4000-2538.07$=$$1522.73$

To test the outcome of the model, compare to see if the sum of savings and required loan is greater than or equal to total expenses.

$z+2500>x$

$1522.73+$2500>4000 i.e.

$4022.73>4000 this show that the expenses can be taken care of by the loan and the savings