Science:Math Exam Resources/Courses/MATH105/April 2010/Question 05 (a)

MATH105 April 2010

  •  Q1 (a)  •  Q1 (b)  •  Q1 (c)  •  Q1 (d)  •  Q1 (e)  •  Q1 (f)  •  Q1 (g)  •  Q1 (h)  •  Q1 (i)  •  Q1 (j)  •  Q1 (k)  •  Q1 (l)  •  Q1 (m)  •  Q1 (n)  •  Q2  •  Q3  •  Q4  •  Q5 (a)  •  Q5 (b)  •  Q5 (c)  •  Q6  •  

   Other MATH105 Exams

  •  April 2009  •  April 2011  •  April 2010  •  April 2012  •  April 2013  •  April 2014  •  April 2015  •  April 2016  •  April 2017  •  April 2018  •  

Question 05 (a)

A person purchased a home at the price of $ 300,000, paid a down payment equal to 20% of the purchase price, and financed the remaining balance with a 25 year term mortgage. Assume that the person makes payments continuously at a constant annual rate $A$ and that the interest is compounded continuously at the rate of 5%. Write down the differential equation that is satisfied by the amount $y(t)$ of money owed on the mortgage at time $t$.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
How can we use a differential equation to model the rate of the amount of money owed, ${\frac {{\textrm {d}}y}{{\textrm {d}}t}}$? What are the factors that increase the amount of money we owe? What are the factors that decrease it?

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work. If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work. If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. At any given time, two things are happening: the owed money is growing at a rate of 5% and the amount of money is going down at a rate of A. Therefore, we write: ${\frac {dy}{dt}}=0.05y-A$. As an initial condition, we impose that $y(0)=0.8\times 300,000=240,000$ i.e. the amount owed is eighty percent of the purchase price since twenty percent was initially paid.

Click here for similar questions

MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Continuous compound interest, Pages using DynamicPageList3 parser function, Pages using DynamicPageList3 parser tag