Lecture 8Discount Interest
Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k/
Math 1140 Financial Mathematics
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Homework 3 was:A) Too hardB) HardC) Just rightD) EasyE) Too easy
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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.
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Grading ScaleGreat job
Good jobMinor mistakes
You have some studying to do.
Serious studying needed.
Come to office hours
Make an appointment to see me.
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Questions?
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Discount InterestAmount = money borrowedDiscount = charge for the use of moneyProceeds = money received from the loanDiscount rate = percent of the amount used to calculate the discountTerm = length of the loan in units of time
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The Basic Discount Interest Formula
D = SdtWhere 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!
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P = S - DWhere 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
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The discount proceeds formula
P = S(1-dt)A) Moves money in
forward in timeB) Moves money
backwards in timeC) Keeps the money putD) Moves the money to
Walmart
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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.
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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) $7,368.42B) $7,000C) $6,650D) I whish I know.E) Who cares?
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A security that matures in 6 months at $7,000 is sold at a discount rate of 10%. How much does the buyer pay?
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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).
dt
PS
1
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A) Crystal clearB) I’m fineC) Not so clearD) I have no idea what
that is
Discount Amount Formula
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The discount amount formula
A) Moves money in forward in time
B) Moves money backwards in time
C) Keeps the money putD) Turns the money into
cheese
dt
PS
1
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Please don’t email 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 email 1)to ask questions about lectures and homework 2) to let me know if something is going on with you3)missing or misreported grades
Email Communication
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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 email me.
Office hours are your best bet that I will remember and record what you said.
Oral Communication
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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
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What is the interest rate of a simple interest loan given the principal, the maturity value and the term?
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Coupon equivalent is the simple interest rate of a loan that charges the same interest as a given discount loan.
Coupon Equivalent
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Find the coupon equivalence of a 12-week bank discount rate of 8%.
Example
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A) Crystal clearB) I’m fineC) Not so clearD) I have no idea what
that is
Coupon Equivalent
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Find the term of a loan taken out in February 2011 and due in July 2011.
Find the term of a loan taken out in February 2011 and due in January 2012.
Calculating terms
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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 3
1+5 ≡ 6 ≡ 0 mod 3
1-5 ≡ -4 ≡ 2 mod 3
Modular Arithmetic
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Find the term of a loan taken out in February 2011 and due in January 2012.
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?
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Find the term of a loan taken out in February 2011 and due in January 2013.
February is the second month.January is the first month.The term is 1-2 ≡ -1 ≡ 11 mod 12
Be careful
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Find the term of a loan taken out in February 2011 and due in January 2012.
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?
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S = P(1+it)P = $10i = 10%
S(t) = 10(1+0.1t)
Future value
Wolfram Alpha command plot [10(1+0.1t), {t , 0 , 10}]
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S = $20i = 10%
Present value
it
SP
1
ttP
1.01
20)(
Wolfram Alpha command plot [20/(1+0.1t), {t , 0 , 10}]
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plot [14.4/(1+0.1t), 10(1+0.1t), {t , 0 , 10}]
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Compare the values:1) Money moved 1 year forward2) Same money movedforward two years and then move them one year backwards.
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Quiz MondayEverything we covered up then except credit card interest.MondayRead sections 2.2, 2.3, 2.4WednesdayHomework 4 is due.
First Exam (max 15 points): 26 September 2011 at 7pm Location to be announced
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