4. Simple Discount Interest.ppt 5s104i

SIMPLE DISCOUNT INTEREST 1

Objective: Today you are expected to learn :  

The basic concept on simple discount interest how to compute for discount rate, term, amount of the loan, and proceeds

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DISCOUNT INTEREST - Discount interest is an amount paid for borrowing money. - is charged at the time the loan that has been negotiated is executed.

Example: I sign today a loan for one year with a maturity value of P100, 000 and receives P90, 000 today as its principal or its proceeds. P10,000 is referred to as the discount interest. 3

DISCOUNT INTEREST (Id) Discount interest depends on three factors: 1.) F = maturity value of the loan, which is the amount of the loan applied for on the origin date 2.) d = the discount interest rate, expressed in percent and to be computed on F 3.) t = the term of the loan Id = F d t 4

DISCOUNT INTEREST (Id) Proceeds – is the amount received by the borrower on the origin date (principal) - is the amount received by the borrower after removing the interest on the loan. - is the difference between maturity value and discount interest. P = F – Id = F – Fdt = F (1 – dt) 5

Connect it algebraically… From Id=Fdt, we can derive the following formulas: Id I Fdt d F For F: I d  Fdt  dt dt dt

For t: I d  Fdt

I d Fdt  Fd Fd

For d: I d  Fdt

I d Fdt  Ft Ft

Id t Fd Id d Ft

P  Proceeds F  I d is the amount received by the borrower For P: Since after removing the interest on the loan, then we will  F  Fdt  F (1  dt) have P =F - I d

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DISCOUNT INTEREST (Id) Example: Basty borrowed P150,000 from Bank Karote for a term of one year. The interest charged is 10% simple discount rate. Find the proceeds of the loan.

Given:

F=P150,000 d=10%=0.10 t=1 P=? Which of the following formulas will we use?

Id F dt

Id t Fd

Id d Ft

P  F  Id

 F (1  dt) 7

DISCOUNT INTEREST (Id) Example: Basty borrowed P150,000 from Bank Karote for a term of one year. The interest charged is 10% simple discount rate. Find the proceeds of the loan. Given: F=P150,000 d=10%=0.10 t=1 P=?

Formula: P  F (1  dt) Solution: P  150,000(1  (0.10)(1))

 150,000(0.9)

 P135,000

Therefore, Basty will receive P135,000 as proceeds of his loan. Professor: Em Gargoles/egg

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DISCOUNT INTEREST (Id) Example: How much should Badong borrow to have P15,000 today if he promised to pay it in 2 years at 6 3/7 % simple discount rate?

Given:

P=P15,000 d=6 3/7%=0.064285714 t=2 F=? Which of the following formulas will we use?

Id F dt

Id Id P t F d  Fd 1  Ft dt

P  F  Id

 F (1  dt) 9

DISCOUNT INTEREST (Id) Example: How much should Badong borrow to have P15,000 today if he promised to pay it in 2 years at 6 3/7 % simple discount rate? Given: P=P15,000 d=0.064285714 t=2 F=?

P Formula: F  1  dt

15,000 Solution: F  (1  (0.064285714 )(2))  P17,213.11 Therefore,Badong needs to borrow P17,213.11 10

DISCOUNT INTEREST (Id) Example: How long should P75,000 be discounted to have a proceeds of P50,000 at 12.6% simple discount rate?

Given:

F=P75,000 P=P50,000 d=12.6%=0.126 t=? Which of the following formulas will we use?

Id F dt

Id t Fd

Id d Ft

P  F  Id

 F (1  dt) 11

DISCOUNT INTEREST (Id) Example: How long should P75,000 be discounted to have a proceeds of P50,000 at 12.6% simple discount rate? Given: F=P75,000 P=P50,000 d=0.126 t=?

Id F  P Formula: t   Fd Fd

25 , 000 ( 75 , 000  50 , 000 ) Solution: t   75,000(0.126) 75,000(0.126)

 2.65 Therefore,it would take 2.65 years to discount P75,000. 12

DISCOUNT INTEREST (Id) Example: Determine the discount rate if P32,000 is the proceeds of a loan of P43,000 due in 16 months.

Given:

P=P32,000 F=P43,000 t=16/12 d=? Which of the following formulas will we use?

Id F dt

Id t Fd

Id d Ft

P  F  Id

 F (1  dt) 13

DISCOUNT INTEREST (Id) Example: Determine the discount rate if P32,000 is the proceeds of a loan of P43,000 due in 16 months. Given: P=P32,000 F=P43,000 t=16/12 d=?

Id F  P Formula: d   Ft Ft

11 , 000 ( 43 , 000  32 , 000 ) Solution: d   43,000(4 / 3) 43,000(16 / 12)

 0.1919 x100  19.19% Therefore, the simple discount rate is about 19.19%. 14

TRY THIS! 1.) The proceeds of a 2-year loan Martha obtained at a bank were P2, 250. If the discount interest rate was 12 ½ %, how much is the maturity value of the loan? F = P3,000 2.) How much should Dwain borrow to have P15,000 today if he promised to pay it in 2 years at d=6 & 3/7%? F= P17, 213.11

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TRY THIS (1/4 SHEET OF Y.PAD) Find the amount due at the end of 15 months if the present value is Php18,000 and if a) the discount interest rate is 5% b) the simple interest rate is 5% P F 1  dt 18,000  1  (.05)15 12   F  Php19,200

F  P(1 rt)

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 18,000 1 (.05)15 12   Php19,125

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1.2  Discount Interest