# Math 210: Theory of Interest (“Financial Mathematics I”) Professor Rick Gorvett 374 Altgeld Hall University of Illinois at Urbana-Champaign Fall 2014.

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Math 210: Theory of Interest (“Financial Mathematics I”) Professor Rick Gorvett 374 Altgeld Hall University of Illinois at Urbana-Champaign Fall 2014

Syllabus Office Hours: 3-4 pm Tuesdays, 3-4 pm Wednesdays, or by appointment Textbook: Mathematical Interest Theory by Vaaler and Daniel (2009, 2 nd Edition) Exam dates: 3 exams, per syllabus Grades: Exams, homeworks, other assignments

Me Director of the UIUC Actuarial Science Program MBA (University of Chicago) Ph.D. in Finance (UIUC) FCAS: Fellow of the CAS ASA: Associate of the SOA CERA: Chartered Enterprise Risk Analyst Actuarial corporate / consulting experience (I wish)

Class Objectives Understand the mathematical foundations of finance Learn Exam 2 / FM material Appreciate this material in a broad, cross- disciplinary framework

Motivation for the Theory of Interest Borrowing and investing –There is a “price” associated with such transactions –I borrow \$1 from you for one day; how much do you want in return? –What about borrowing for 1 year? 5 years? 10 years? –What about borrowing \$10? \$100? \$1,000? \$10,000?

Motivation for the Theory of Interest (cont.) 1 yr 5 yrs10 yrs… Time Horizon Amount \$ 1 10 100 1,000 10,000 Increasing “Charge”

Definitions of “Interest” “Interest may be defined as the compensation that a borrower of capital pays to a lender of capital for its use.” –Kellison, The Theory of Interest, p. 1 Interest is “the time value of money” –Broverman, Mathematics of Investment and Credit, p. 1 “Cost of using money.” –Dictionary of Finance and Investment Terms, p. 203

Historical / Cultural Context “And if your brother becomes poor…. you shall not lend him your money at interest.” –Old Testament, Leviticus 25:35-37 “You shall not lend upon interest to your brother…. To a foreigner you may lend upon interest, but to your brother you shall not lend upon interest.” –Old Testament, Deuteronomy 23: 19-20

Historical / Cultural Context “The most hated sort (of wealth-getting), and with the greatest reason, is usury, which makes a gain out of money itself, and not from the natural object of it. For money was intended to be used in exchange, but not to increase at interest.” –Aristotle, Politics Book 1, Ch. 10 “Usury”: lending money at an unreasonably high interest rate

Historical / Cultural Context “(A group)…. systematically increased its wealth by usury in defiance of a law passed by Caesar the Dictator…. First, the Twelve Tables prohibited anyone from exacting more than 10% when, previously, the rate had depended on the caprice of the wealthy. Subsequently,…. interest was reduced to half that amount, and finally compound interest was wholly forbidden.” –Tacitus, The Annals Book 6, Ch. 16

Historical / Cultural Context “…. you may avoid usury by a simple shift of the intention. ‘It would be downright usury,’ says he, ‘to take interest from the borrower, if we should exact it as due in point of justice; but if only exacted as due in point of gratitude, it is not usury….’ ” –Pascal, Provincial Letter VIII

Historical / Cultural Context “The lowest ordinary rate of interest must…. be something more than sufficient to compensate the occasional losses to which lending, even with tolerable prudence, is exposed.” –Adam Smith, The Wealth of Nations

Historical / Cultural Context While studying, especially for actuarial exams, keep in mind a quote: “Do you think that you shall enter the Garden of Bliss without such trials as came to those who passed away before you?” –Joseph Campbell, The Power of Myth – quote from the Quran (Koran),

Data per FRED, St. Louis FRB, for 3-Month T-Bills, Secondary Market

In This Class… We tend to refer to the (one) interest rate –In reality, there are many interest rates We tend to assume interest rates do not change –In reality, interest rates are stochastic

Typical Interest Theory Problem Four quantities If you know three, you can determine the fourth 1)Initial value 2)Interest rate 3)Time period 4)Final value 1 4 2 3

Next Time… Begin discussing interest rates Accumulation and amount functions Simple versus compound interest Effective versus nominal interest

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