Algebra 2 question for the smart!?

Question

A student borrowed money for medical school costs. There is no interest. After 61 monthly payments, the loan balance was $24,563. After 77 monthly payments, the loan balance was 17,891. What are the values and the meaning of the slope of the line representing the loan balance? What was the original amount of the loan?

Answer 1

You have two variables: time and balance. So first you have to think in this manner of calling the time passed X and the balance owed Y. Now you can graph it.

When X = 61 months, Y = $24,563

When X = 77 months, Y = $17,891

Please note that this is the reason that we learn algebra. We assign variables to existing quanties, and study the relation.

Now recall that slope is defined often as "rise over run." The "rise" is the change in why for a corresponding "run" that is a change in X.

Now notice that Y has units of dollars, and X has units of months. If you find the slope, you are dividing money by time. Hence, the slope is in units of dollars per month. This would be the monthly payment made on the balance.

In this case, the rise--being a change in Y--is the amount of money paid between the two points. Take the vaue for the second point and subtract the value for the first point. The difference is $17,891 -$24,563 = -$6,672. The run is the amount of time between points, being 77 months - 61 months = 16 months. Divide the rise by the run.

-$6,672/16 months = -$417/month. So the slope here is NEGATIVE because the balance goes down with time.

The original amount of the loan can be found by using the slope. We put the equation in y = m*x + b form, where m is the slope and b is the y-intercept. However, we don't yet know the y-intercept. So instead we plug in values for X and Y. What we get is:

24,563 = (-417)*(61) + B
24,563 = -25,437+ B

Add 25,437 to both sides, and it cancels out on the right:

24,563 + 25,437= -25,437) + 25,437 + B
50,000 = 0 + B = B

So the y-intercept is B = $50,000.

If we plug these values into the y = m*x + b equation, we find

y = -417*x + 50,000

To find the initial balance, we plug in X = 0, which would be time zero--before payments are made. This gives that

For X = 0
Y = (-417)*0 + 50,000

or Y = 50,000

So at time zero, Y = $50,000. This is the initial amount owed.

Hoped you followed all of that. make sure to follow the reasoning and do the math again, because I might have made a small arithmetic error just to keep you honest.

Good luck. ;)

Answer 2

First you have to figure out how much was paid off in between the 61st payment and the 77th payment, just subtract the values from each other.
$24,563- $17891=$6672
We know that that was over 11 payments, so divide $6672 by 16
$6672/16=$417

That gives you how much each payment was.
Then divide the remainder of the loan by the payment amount.
$17891/$417=42.9 payments
Now add that number to the number of payments that have already been paid to get how many payments were in the whole life of the loan.
42.9+77=119.9
That's how many payments there were, now multiply that by the payment amount and you will have the loan amount.
119.9 payments x $417= $50000 and that's how much was borrowed, use a graphing calculator to figure out the slope. I have no clue about that, i didn't pay attention in that part of class


I had to go back and change it because for some reason i got one number wrong and of course the screwed the whole thing up, but now it is correct

Answer 3

To complete the problem you must first get the amount of one months payment, Do: 24563-17891, This will give you the amount paid between month 61 and month 77. Then divide by 16, the number of months. This gives you $ 417. You then multiply that by 61 and add it to 24563 to give you the total or original loan amount. Let y= the loan balance and Let x= the number of payments made (the number of months)

This gives you the formula:
y= -417x + 50,000 or y= 50,000 - 417x
- 417=the amount of dollars paid per month is the slope, while the slope does not change it is not equal to 1 because that would mean that the student pays 1 dollar per month. A slope of negative 417 means that the student lowers the loan amount by $ 417 a month.
yintercept = 50,000 which is the total amount of the loan.

Answer 4

Let y be the amount that he initially borrowed and x be the monthly payment.

Then

y - 61x = 24563

and

y - 77x = 17891

If you solve the above two equation for y and x, you can see that the total amount borrowed is 50,000 and monthly payment is 417.

I think since the payments were constant, then the slope should be 1.

Answer 5

wow! I shoulda stayed in school. (and I thought I was smart)