Lecture 8 Discount Interest Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140...

Lecture 8Discount Interest

Ana Nora Evans 403 [email protected]://people.virginia.edu/~ans5k/

Math 1140 Financial Mathematics

Math 1140 - Financial Mathematics 2

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4Math 1140 - Financial Mathematics


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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


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!


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


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


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.


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?


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


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


A) Crystal clearB) I’m fineC) Not so clearD) I have no idea what

that is

Discount Amount Formula


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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Oral Communication


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


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


Coupon equivalent is the simple interest rate of a loan that charges the same interest as a given discount loan.

Coupon Equivalent


Find the coupon equivalence of a 12-week bank discount rate of 8%.

Example


A) Crystal clearB) I’m fineC) Not so clearD) I have no idea what

that is

Coupon Equivalent


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


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



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?




Be careful



Do mod 12 arithmetic.


How can we use it?


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}]


S = $20i = 10%

Present value

it

SP

1

ttP

1.01

20)(

Wolfram Alpha command plot [20/(1+0.1t), {t , 0 , 10}]


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


Compare the values:1) Money moved 1 year forward2) Same money movedforward two years and then move them one year backwards.


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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Lecture 8 Discount Interest Ana Nora Evans 403 Kerchof [email protected] ans5k/ Math 1140...

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