Lecture 8 Discount Interest Ana Nora Evans 403 Kerchof Math 1140 Financial Mathematics

Math Financial Mathematics Homework 3 was: A)Too hard B)Hard C)Just right D)Easy E)Too easy 2

Math Financial Mathematics I did not come to office hours because: A)The homework was easy. B)I can’t make it. C)I started too late. D)It’s siesta time. E)What are you talking about, I came to office hours. 3

Math Financial Mathematics 4

Grading Scale Great job Good job Minor mistakes You have some studying to do. 5 Serious studying needed. Come to office hours Make an appointment to see me.

Math Financial Mathematics Questions? 6

Math Financial Mathematics Discount Interest 7 Amount = money borrowed Discount = charge for the use of money Proceeds = money received from the loan Discount rate = percent of the amount used to calculate the discount Term = length of the loan in units of time

Math Financial Mathematics The Basic Discount Interest Formula D = Sdt Where D is the discount S is the amount (future value) d is the discount rate t is the term This is the formula for calculating the discount! 8

Math Financial Mathematics P = S - D Where P is the proceeds D is the discount S is the amount (future value) Calculates how much the borrower receives. P = S - D = S - Sdt = S(1-dt) Discount Proceeds Formula 9

Math Financial Mathematics The discount proceeds formula P = S(1-dt) A)Moves money in forward in time B)Moves money backwards in time C)Keeps the money put D)Moves the money to Walmart 10

Math Financial Mathematics 11 The value of money that we know is the amount S. We calculate the proceeds P at the due date. Thus we are moving S backwards in time from the due date to the loan date.

Math Financial Mathematics A security that matures in 6 months at $7,000 is sold at a discount rate of 10%. How much does the buyer pay? A) $7, B) $7,000 C) $6,650 D) I whish I know. E) Who cares? 12

Math Financial Mathematics 13 A security that matures in 6 months at $7,000 is sold at a discount rate of 10%. How much does the buyer pay?

Math Financial Mathematics Discount Proceeds Formula P = S(1-dt) Discount Amount Formula Calculates the amount( S ) given the proceeds( P ), the discount rate( d ), and the term(t). 14

Math Financial Mathematics A)Crystal clear B)I’m fine C)Not so clear D)I have no idea what that is Discount Amount Formula 15

Math Financial Mathematics The discount amount formula A)Moves money in forward in time B)Moves money backwards in time C)Keeps the money put D)Turns the money into cheese 16

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Math Financial Mathematics Please don’t me about things that you can find by asking one your classmates(eg where do I buy the clicker, where do I register my clicker,…) Please use 1)to ask questions about lectures and homework 2) to let me know if something is going on with you 3)missing or misreported grades Communication 18

Math Financial Mathematics Before class, I need to get my many toys ready. After class, I am tired and very unlikely to remember what you told me. Please me. Office hours are your best bet that I will remember and record what you said. Oral Communication 19

Math Financial Mathematics Discount interest loan with discount rate d, amount S, term t. The proceeds P = S(1-dt). What is the interest of a simple interest loan with principal equal to the proceeds, maturity value equal to the amount and same term? Discount vs Simple Interest 20

Math Financial Mathematics What is the interest rate of a simple interest loan given the principal, the maturity value and the term? 21

Math Financial Mathematics Coupon equivalent is the simple interest rate of a loan that charges the same interest as a given discount loan. Coupon Equivalent 22

Math Financial Mathematics Find the coupon equivalence of a 12-week bank discount rate of 8%. Example 23

Math Financial Mathematics A)Crystal clear B)I’m fine C)Not so clear D)I have no idea what that is Coupon Equivalent 24

Math Financial Mathematics Find the term of a loan taken out in February 2011 and due in July Find the term of a loan taken out in February 2011 and due in January Calculating terms 25

Math Financial Mathematics a ≡ b mod n if a and b give the same remainder when divided by n. a+b ≡ (a+b) mod n a-b ≡ (a-b) mod n 1 ≡ 4 mod 3 -1 ≡ 2 mod ≡ 6 ≡ 0 mod ≡ -4 ≡ 2 mod 3 Modular Arithmetic 26

Math Financial Mathematics Find the term of a loan taken out in February 2011 and due in January Do mod 12 arithmetic. February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 How can we use it? 27

Math Financial Mathematics Find the term of a loan taken out in February 2011 and due in January February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 Be careful 28

Math Financial Mathematics Find the term of a loan taken out in February 2011 and due in January Do mod 12 arithmetic. February is the second month. January is the first month. The term is 1-2 ≡ -1 ≡ 11 mod 12 How can we use it? 29

Math Financial Mathematics S = P(1+it) P = $10 i = 10% S(t) = 10(1+0.1t) Future value 30 Wolfram Alpha command plot [10(1+0.1t), {t, 0, 10}]

Math Financial Mathematics S = $20 i = 10% Present value 31 Wolfram Alpha command plot [20/(1+0.1t), {t, 0, 10}]

Math Financial Mathematics plot [14.4/(1+0.1t), 10(1+0.1t), {t, 0, 10}] 32

Math Financial Mathematics Compare the values: 1)Money moved 1 year forward 2) Same money moved forward two years and then move them one year backwards. 33

Math Financial Mathematics Quiz Monday Everything we covered up then except credit card interest. Monday Read sections 2.2, 2.3, 2.4 Wednesday Homework 4 is due. First Exam (max 15 points): 26 September 2011 at 7pm Location to be announced Charge 34