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Midterm

# MAT133 Midterm 1 Test Breakdown and Analysis

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Department
Mathematics
Course Code
MAT133Y1
Professor
all

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Exam Analysis: MAT133, Midterm 1 1) TEST BREAKDOWN: The five major topics covered for midterm 1 were compound interest, annuities, amortization, bonds and matrices. The test is usually 1 hour and 50 minutes, and worth 100 points. - Part A. Multiple Choice o The questions here are all worth 4 marks and they are very straight forward. o They usually cover the topics of  Converting interest rates  Manipulating amortization formula and search for unknown  Manipulating bonds formula and search for unknown  Multiplication rule of matrices  Matrices reduction - Part B. Written-Answer Questions o There are three questions that requires you to show your work in details and they are worth 15 marks each. They will be less straight forward and will require more in depth understanding of topics o They usually cover the topics of  Mortgage related questions  Finding inverse or solving system of equations with matrices  Solving real life problems with matrices (system of equations)  Amortization questions with a high probability of asking for amount of payment at n-time 2) TEST STATISTICS Topics 2008 2009 2010 2011 2012 Total Interest rates 2 2 1 1 1 7 Annuities 2 1 2 1 1 7 Amortization 2 3 4 3 2 14 Perpetuity 0 0 1 1 1 3 Bonds 2 2 1 1 2 8 Matrices operations 5 5 4 6 6 26 Solving real life problems 1 1 1 1 1 5 with matrices 3) KNOWLEDGE SUMMARY Interest rates Compound Interest Formula For an original principal of P, the formula 𝑆 = 𝑃 1 + 𝑟 )𝑛 gives the compound amount S at the end of n interest periods at the periodic rate of r. Effective Rate The effective rate r that is equivalent to a nominal rate of r compounded n times a year is given by 𝑟 𝑛 𝑒 = (1 + ) − 1 𝑛 Present Value The principal P that must be invested at the periodic rate of r for n interest periods so that the compound amount is S is given by 𝑷 = 𝑺 𝟏 + 𝒓 )−𝒏 And is called the present value of S Annuities Present Value of an Annuity The formula 1 − 1 + 𝑟 )−𝑛 𝐴 = 𝑅 × = 𝑅 × 𝑎 𝑛|𝑟 𝑟 Gives the present value A of an ordinary annuity of R per payment period for n periods at the interest rate of r per period Future Value of an Annuity The formula (1 + 𝑟 )𝑛 − 1 𝑆 = 𝑅 × = 𝑅 × 𝑠 𝑛|𝑟 𝑟 Gives the future value S of an ordinary annuity of R (dollars) per payment period for n periods at the interest rate of r per period Amortization Periodic payment 𝐴 𝑟
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