[LEC]2.2 Discount Interest

8/8/2019 [LEC]2.2 Discount Interest

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Business MathematicsDe La Salle University

Concept of Discount Interest

Comparing Simple and Discount Interest

Computing for

Discount Interest Proceeds

Maturity Value

Discount Rate

Term


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TRIVIA:

Five Six is a common lending practice in

urban and sub-urban areas often

associated to some Indian Nationals thatmigrated here in the Philippines.

Five Six is based on discount interestwhere Php1 is charged for every Php5

borrowed.


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Note: The amount of the loan applied for on

the origin date is the amount due on

the maturity date.

Amount (Id) paid for borrowing money

charged in advance and is taken from

the amount of the loan applied for on

the origin date.

DISCOUNT INTEREST


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Is - simple interest

r - simple interest rate

Id - discount interest

d - discount interest rate

NOTATION


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Note: Discount Interest is dependent on

- Maturity value (amount of the loan)

- discount interest rate

- term of the loan

DISCOUNT INTEREST

FdtId!


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Note: For this reason, discount interest is

often referred to as interest charged in

advance.

Amount (P) received by the borrower

after deducting the discount interest on

the origin date, and is also referred to as

the discounted amount.

PROCEEDS


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PROCEEDS

dIFP )1( dtFP !

MATURITY VALUE

dIPF

dt

IF

d

dtF

1


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TERM

Fd

It

d!

Fd

Ft

!

DISCOUNT INTEREST RATE

Ft

Idd

!

Ft

Fd

!


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1. Solve for F and d given

P = Php24 375, I = 625, t = 120 days

2. Solve for F and I given

P = Php9 750, d = 15%, t = 15 months

3. Solve for I and d

P = Php14 500, F = Php15 000, d = 250 days

4. Solve for I and t given

P = Php90, F = Php100, d = 0.16


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1. Solve for F and d given

F = Php25 000, d = 7.5%

2. Solve for F and I given

F = Php12 000, I = Php2 250

3. Solve for I and d

I = 500, d = 4.8%

4. Solve for I and t given

I = Php10, t = 0.625 = 7MOS, 15 DAYS


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Discount Interest (Id)

- interest charged in advance

- discount amount

Principal (P)

- proceeds

- amount after discounting

- discounted amount

- amount received at the origin date


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Maturity Value (F)

- amount of the loan

- amount received at the maturity date

Discount Interest Rate (d)

Term (t - express in years)


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1.Tito borrows Php20 000 from SSS for a term

of 1 year. The interest charged is 5%

discount interest rate. Determine theproceeds of the loan made by Tito.


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G: F = Php20 000, t = 1, d = 0.05

R: P

E:

S: P = 20 000(1 (0.05)(1))

A: P = Php19 000

)( dtP !


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2. The proceeds of a two-year loan is

Php12 160. If the discount interest rate is

12%, how much is the maturity value ofthe loan?


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G: P = Php12 160, t = 2, d = 0.12

R: F

E:

S:

A: P = Php16 000

)1( dtFP !

)2)(12(.1

12160

!F


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3. The proceeds of a Php12 000 cooperative-

loan is Php11 675. If the term of the loan

is from January 15 to June 14, 2009, atwhat rate was the interest charged?


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G: F = Php12 000, P = Php11 675

OD = Jan 15, 09, MD = Jun 14, 09

R: d

E:

S: t = 150 days

d = (12000-11675) / (12000x150/360)

A: d = 6.5%

FdtI !

PFI !


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G: F = Php15 000, P = Php12 000, d = 0.09

R: t

E: I = Fdt

I = F - PS: t = (15000-12000) / (14000x0.09)

t = 2.22222222 =>2 YRS

0.22222x12 = 2.66667 = 2 MOS

0.66667x30 = 20 DAYS

A: 2 YRS, 2 MOS and 20 DAYS


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1. If Php10 000 is due on December 16, 2008,find the proceeds on April 20, 2008, if the

discount interest rate is 12%.

2. Find the discount interest rate if Php7 200 isthe present value of Php8 000 due in 15

months.

3. Find the term of a loan whose proceeds and

maturity value are Php15 000 and Php16 500

respectively, at a discount interest rate of 8%.

[LEC]2.2 Discount Interest

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