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Math 1140 Financial Mathematics Lecture 3 More about Simple Interest Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k/ Slide 2 Math 1140 - Financial Mathematics Registration Survey Diverse mathematical backgrounds Some really funny answers Fairly diverse interests Most popular reason to take the class is to learn practical math. 2 Slide 3 Math 1140 - Financial Mathematics Practical Math Skills On the homework, use capital letters to write your name. If you bring more than one page use staples or paper clips to keep pages together. Keep the grader (that would be me) happy by writing neatly and clearly. Typing the homework is strongly preferred. 3 Slide 4 Math 1140 - Financial Mathematics Why bother to do it? If you dont I will not grade the homework! 4 Slide 5 Math 1140 - Financial Mathematics Questions? Dont wait until the class is over, ask now! Your classmates will thank you for asking it, because either they did not think about it or they are too shy to ask. 5 Slide 6 Math 1140 - Financial Mathematics Homework grading scale Grades from the highest to lowest: The actual stickers are all smileys, but if you see red or purple is not good at all. I couldnt find frownies. 6 Slide 7 Math 1140 - Financial Mathematics Second Homework 7 Assume you charged $3,000 on the first day of the credit card cycle and you dont pay the balance on time. How much will you pay in finance charges and interest next cycle? Slide 8 Math 1140 - Financial Mathematics Problem 2 8 First billing cycle: 07/13/11 08/12/11 No previous balance. Charge $3,000 on 07/13/11. Second billing cycle: 08/13/11 09/12/11 Bill due on 09/04/11. No payment. Statement issued on 09/13/11. What fees and interest would you see on this second statement? Slide 9 Math 1140 - Financial Mathematics More interesting things to calculate Instead of no payment assume you pay all $3,000 one day late. How much would you pay in interest and fees? 9 Slide 10 Math 1140 - Financial Mathematics Terms from last time Interest I Interest rate i Principal P Term t Maturity value S 10 Slide 11 Math 1140 - Financial Mathematics Formulas I = Pit S = P + I S = P + Pit S = P(1 + it) 11 Slide 12 Math 1140 - Financial Mathematics Today More about how to calculate the term. Add-on loans Discounting a promissory note Present Value 12 Slide 13 Math 1140 - Financial Mathematics Conventions When we say the interest rate is 14% we mean the interest rate is 14% per year. If the time is given in months, we assume all the months have the same length. Example: 3 months = 3/12 years 13 Slide 14 Math 1140 - Financial Mathematics Pledged quiz No collaboration You borrow $5,000 dollars, and the loan charges simple interest. If you owe $5,125 in 6 months, what is the interest rate? A)1% B)2% C)3% D)5% This is a correct/incorrect question. 14 Slide 15 Math 1140 - Financial Mathematics Quiz Problem You borrow $5,000 dollars, and the loan charges simple interest. If you owe $5,125 in 6 months, what is the interest rate? Given: principal: P = maturity value: S = term: t = Unknown (what we need to calculate): interest rate: i = 15 Slide 16 Math 1140 - Financial Mathematics More realistic view Sometimes the term is not given in days, months or years. You are given the date the loan is made and the date the loan is paid. There are different conventions! 16 Slide 17 Math 1140 - Financial Mathematics Counting Days How many days are there from 14 August to September 5? A)9 days B)20 days C)21 days D)22 days E)23 days This is a participation question. 17 Slide 18 Math 1140 - Financial Mathematics How did you calculate? The answer depends on whether you include August 14 or not. In you dont include August 14, you calculate the answer by adding the days in August, 31- 14=17, to the days in September 5, to get 22. If you include August 14, then the answer is 23. 18 Slide 19 Math 1140 - Financial Mathematics Methods for computing the term exact time uses every day of the term, except the first day approximate time assume that every month has 30 days 19 Slide 20 Math 1140 - Financial Mathematics Exact time - Example Find the exact time for a loan taken out on 14 August and due on 5 September. First we calculate how many days in August we count: Second we add the number of days in September: 20 Slide 21 Math 1140 - Financial Mathematics Exact Time Each day has a serial number. Look it up in the serial table at the end of your book. Be careful about leap years! Add 1 if the date is after Feb 29. 21 Slide 22 Math 1140 - Financial Mathematics Exact time t = sn 2 -sn 1 where t is the term sn 2 is the serial number of the due date sn 1 is the serial number of the date the loan was taken. 22 Slide 23 Math 1140 - Financial Mathematics Lets try the serial table Find the exact time for a loan taken out on 14 August and due on September 5. 23 Slide 24 Math 1140 - Financial Mathematics When is the formula wrong? The formula does not work when the two dates fall in different years. 24 Slide 25 Math 1140 - Financial Mathematics The dates fall in different years t = sn 2 + (365 -sn 1 ) where t is the term sn 2 is the serial number of the due date sn 1 is the serial number of the date the loan is taken out. 25 Slide 26 Math 1140 - Financial Mathematics Another example Find the exact time for a loan taken out on 14 August 2011 and due on 5 September 2012. 26 Slide 27 Math 1140 - Financial Mathematics There is nothing funny about simple interest, but there is about grad school 27 Slide 28 Math 1140 - Financial Mathematics Approximate Time This is what the textbook says: The number of months measured from the starting day of a loan to the same day in the month containing the maturity date. Each month is assumed to be 30 days with exact time used for any portion of a month. 28 Slide 29 Math 1140 - Financial Mathematics Compare exact and approximate time A)Exact time always gives more days B)Approximate time always gives more days C)Sometimes exact time gives more days, sometimes approximate time gives more days This is a participation question. 29 Slide 30 Math 1140 - Financial Mathematics Answer The correct answer is C, it depends on the situation. To understand why think about these two situations: -Take out a loan on February 1 with maturity date March 1 -Take out loan on January 1 with maturity date December 10. 30 Slide 31 Math 1140 - Financial Mathematics Life is even messier than I told you The interest rate i is given per year. The term is calculated in days. We need to convert the days to years. Divide by 365. 31 Slide 32 Math 1140 - Financial Mathematics That is logic, this is finance Ordinary interest uses 360 days year Divide the number of days by 360. Exact interest uses 365 days year Divide the number of days by 365. 32 Slide 33 Math 1140 - Financial Mathematics Thinking Time Which interest type is better for the borrower? A)Ordinary interest (divide by 360) B)Exact interest (divide by 365) C)They are the same D)Depends on the term of the loan This is a participation question. 33 Slide 34 Math 1140 - Financial Mathematics Class Answers 34 Slide 35 Math 1140 - Financial Mathematics Discussion 35 Slide 36 Math 1140 - Financial Mathematics Answer I think the answer should be D. Consider the situations -The term is exactly 1 year. In this case, the interests are qual. -The term is 1 day. In this case exact interest is better for the borrower. Depending on your interpretation of better the answer could also be B. See class notes. 36 Slide 37 Math 1140 - Financial Mathematics Possibilities Exact TimeApproximate Time Ordinary InterestBankers RuleTime is given in months or years Exact InterestUsed by credit card companies. Rarely used. 37 Slide 38 Math 1140 - Financial Mathematics Break time 38 Slide 39 Math 1140 - Financial Mathematics Charge Due Monday: Read sections 1.5, 1.6, 1.7 Due Wednesday (31 August): Second homework 39