<p>Hey plz help me with this easy math question!,,,,,!!!
Thanks
Example 2: Loan repayment schedule
The monthly repayment schedule for a 25 year loan with 7% interest per annum depends (is a func- tion of) the total loan. For a loan of $70,000 the monthly repayment is $495, for a loan of $100,000 the monthly repayment is $705. Assuming this function is linear, express the repayments P (x) as a function of the loan x. What is P(90000) and what does it represe</p>
<p>You are given two points on the line: (70,000, 495) and (100,000, 705). The slope of the line is then (705-495)/(100,000-70,000)=7/1000. Let’s use the first point, and write an equation in point-slope form: P - 495=(7/1000)(x - 70,000)</p>
<p>Solving for P gives P(x) = (7/1000)x+985.</p>
<p>Finally, P(90,000) = (7/1000)(90,000)+985 = 1615.</p>
<p>$1615 is the monthly repayment for a loan of $90,000.</p>
<p>Where is that 985 coming from?
And the answer should be around 636!!
I got an answer but I did it like you before I post this question, but it wasn’t working</p>
<p>DrSteve,
I am usually in complete agreement with your posts but this one troubles me. You have a an answer of a monthly payment for 90,000 that is more than twice the monthly payment for 100,000. If I used the slope of .007 and set the equation y=.007x + b, plug in either set of values 495 = (.007)(70,000) + b, I get b = 5. The equation then becomes </p>
<pre><code> y = .007 x + 5
</code></pre>
<p>plugging in 90,000 for x
y = .007 (90,000) + 5
y = 630 + 5
y = 635</p>
<p>Clearly I made a computational error - the hazards of blindly doing computations on your calculator without checking to see if your answer makes sense. Sorry about that. Let me give you the corrected solution followed by some comments:</p>
<p>You are given two points on the line: (70,000, 495) and (100,000, 705). The slope of the line is then (705-495)/(100,000-70,000)=7/1000. Let’s use the first point, and write an equation in point-slope form: P - 495=(7/1000)(x - 70,000)</p>
<p>Solving for P gives P(x) = (7/1000)x+5.</p>
<p>Finally, P(90,000) = (7/1000)(90,000)+5 = 635.</p>
<p>$635 is the monthly repayment for a loan of $90,000.</p>
<p>Remarks: (1) The error in my original post was a missing minus sign when I distributed (7/1000)(x-70,000). After multiplying this becomes (7/1000)x - 490 (in my original post I left out the minus sign).</p>
<p>(2) If I was actually answering this question on a test, there are several ways I would have caught this error.</p>
<p>(a) by glancing back at the question I would have noticed my answer was too big.
(b) I would have plugged the original points in to the equation I got and noticed that they didn’t work.
(c) I would have solved the problem using another method (perhaps pmian’s method above) and saw that the two answers didn’t match up.</p>
<p>(3) If you are allowed to use a calculator for this question you might prefer leaving the fraction 7/1000 as the decimal .007. In this case the point-slope form gives us P - 495= .007(x - 70,000) = .007x - 490. So P = .007x - 490 + 495 = .007x + 5.</p>
<p>(4) We can quickly change from point-slope form to slope-intercept form in one step by distributing .007 on the right hand side and adding 495 to the result</p>
<p>(5) If we weren’t required to rewrite the expression as a funtion of x, and we were only asked to compute P(90,000), then there would be no need to change to slope-intercept form - we could simply plug 90,000 in for x in the point slope form and find P.</p>
<p>If you are looking for a non-algebra solution (and some of us like those…)</p>
<p>It helps to remember that for linear functions, delta Y is always proportional to delta X.</p>
<p>In this case, when the loan amount went from 70,000 to 1000,000 the payment went from 495 to 705. So the loan increased by 30,000 and the payment increased by 210.</p>
<p>Now if you want to find the payment on a 90,000 loan: that increased by only 20,000 from the original loan. In other words, the delta Y was 2/3 of the original change so the delta X also has to be 2/3 of the original increase: 2/3 of 210 is 140. Add 140 to 495 to get 635.</p>
<p>When I started to do this problem this way and I saw that the new increase was 2/3 of the old increase, I was hoping that the x-value would be easy to work with – and it was! 210 is an easy number to take 2/3 of. It’ s as if the author is hoping you’ll do it this way, or at least rewarding you for doing it this way.</p>
<p>Those problems are very easy to solve by simply writing the numbers down and … analyzing the patterns of growth. Obviously the answer will be the SAME as the posts above me, but here is what I do in such cases. </p>
<p>70 > 495
100 > 705
means (by a mere substraction)
30 > 210
or
10 > 70</p>
<p>Which means that 90 > 705-70 or 635.</p>
<p>Fwiw, my working paper only shows the following because I KNOW I wanted to substract the given values. </p>
<p>30 > 210
10 > 70
705 - 70 = 635</p>
<p>Does anybody know which free response question had the answer 155? I just don’t remember the question</p>
<p>Thanks everyone! Yeh i worked before like xiggi as well! But i wanted to work using linear function stuff! I guess! I got an answer, and i just wanted to see how people can work different way! anyway thanks everyone</p>