BUSANA1 Chapter1 - Simple Interest and Discount

Simple Interest and Discount Christopher F. Santos

BUSANA1 Chapter 1 De La Salle University 2nd Term 2015-16

Christopher F. Santos

Simple Interest and Discount

DLSU BUSANA1 Chapter 1

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Interest

Interest is a benefit in the form of a fee that the lender/creditor receives for letting the borrower use his money. TWO TYPES: 1 Simple Interest 2 Compound Interest - will be discussed in the next chapter




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Important Dates in Lending

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Origin Date (O.D.) - date on which borrowed money is received by borrower Maturity Date (M.D.) - date on which the loan is to be completely repaid




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Factors Affecting Simple Interest I

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2

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principal P - amount of money borrowed or invested interest rate r - annual rate (in percent) charged by the lender term of the loan t - number of years the sum of money was borrowed or invested I = Prt




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Example

How much simple interest is charged when 100PhP is borrowed for 3 years with an interest rate of 10%? Solution: I =? P = 100PhP r = 10% = 0.10 t =3


) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Example



) I = Prt = (100)(0.10)(3) = 30



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Maturity/Future Value F

- amount to be received by the lender from the borrower on the maturity date F =P +I F = P + Prt F = P(1 + rt)




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Examples

1. How much should the borrower pay the lender after 3 years if he borrowed 100PhP at an interest rate of 10%? ANS. 130PhP 2. In how much time will 28,000PhP amount to 29,134PhP at 16.2% simple interest rate? ANS. 0.25 years or 3 months




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Examples





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Examples

3. At what simple interest rate will a sum double itself in 5 years? ANS. 20% 4. What principal will amount to 6,750PhP in 2 years and 6 months at 8% simple interest rate? ANS. 5,625PhP




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Examples





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Examples





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Computing I when t is in months

If the term t is given in months, convert it first to years before applying the formulas. P r (per yr) t I F 7,200 (1) 7 months 352.80 (2) 6,800 0.156 (3) (4) 8,568.00 3 (5) 12 4 % (6) 948.28 9,448.28




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Computing I when t is in days D

1

Ordinary Interest - t =

2

Exact Interest - t =


D (default) 360

D 365



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Example

Find the amount if 8,000PhP is invested for 250 days at 14% simple interest rate using 1

exact interest

ANS. 8,767.12PhP

2

ordinary interest

ANS. 8,777.78PhP




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Example


exact interest

ANS. 8,767.12PhP

2

ordinary interest

ANS. 8,777.78PhP




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Example


exact interest

ANS. 8,767.12PhP

2

ordinary interest

ANS. 8,777.78PhP




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Counting Days Between Two Dates (O.D. and M.D.)

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Actual Time - we count everyday, except the origin date, within the term Approximate Time - we assume every month consists of 30 days

Example: Find the actual and approximate time from January 21, 2016 to June 19, 2016. ANS. The actual time is 150 days while the approximate time is 148 days. Christopher F. Santos



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Computing Term Between Two Dates

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ordinary interest, actual time - the default and a.k.a. the Banker’s Rule ordinary interest, approximate time exact interest, actual time exact interest, approximate time NOTE: 1 2

The Banker’s Rule gives the highest interest. If the day of the dates are the same, then we count in months.




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Examples

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O.D.: June 25, 2011 M.D.: December 25, 2011 ) t = 6 months = 0.5 years O.D.: February 9, 2011 t = 3 months = 0.25 years ) M.D.: May 9, 2011




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Examples

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O.D.: June 25, 2011 M.D.: December 25, 2011 ) t = 6 months = 0.5 years O.D.: February 9, 2011 t = 3 months = 0.25 years ) M.D.: May 9, 2011




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Examples

OIAcT EIApT EIAcT OIApT EIApT OIAcT


O.D. Days M.D. t 2/18/12 120 (1) (2) 2/18/12 (3) 6/18/12 (4) 2/18/12 (5) 6/18/12 (6) 2/18/12 120 (7) (8) 10/31/10 120 (9) (10) 3/6/11 (11) 8/11/11 (12)



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Examples 1. Find the amount of 10,000PhP on December 15, 2009 if it was invested on March 15, 2009 at 5.04% simple interest rate. ANS. 10,378PhP 2. Find the maturity value of 18,000PhP if it is invested from February 10, 2008 to April 16, 2009 at a simple interest rate of 15%? ANS. 21,232.50PhP Christopher F. Santos



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Present Value

- another name/terminology for the principal P - current value of an amount F that is due at some future date F = P(1 + rt) P=


F 1 + rt



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Present Value

- another name/terminology for the principal P - current value of an amount F that is due at some future date F = P(1 + rt) P=


F 1 + rt



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Examples

The question What principal will amount to 6,750PhP in 2 years and 6 months at 8% simple interest rate? can be restated as What is the present value of 6,750PhP due in 2 years and 6 months if money is worth 8% simple interest?




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Examples 1. In order to have 163,200PhP three years from now, how much must a business invest today if the simple interest rate is 18% per annum? ANS. 105,974.03PhP 2. To pay a debt, Pong offered Bert 1,000PhP now or 1,100PhP three months from now. If saving account simple interest is 10%, which offer will give better return for Bert? ANS. 1,100PhP in 3 months Christopher F. Santos



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Discount Interest/Simple Discount Id -interest collected/deducted in advance (on O.D. instead of on M.D.) Factors Affecting Id : 1 2

3

maturity value F - loan amount applied for discount interest rate d - interest rate (in percent) charged in advance term of the loan t - time between O.D. and M.D. Id = Fdt Christopher F. Santos



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Discount Interest/Simple Discount Id -interest collected/deducted in advance (on O.D. instead of on M.D.) Factors Affecting Id : 1 2

3

maturity value F - loan amount applied for discount interest rate d - interest rate (in percent) charged in advance term of the loan t - time between O.D. and M.D. Id = Fdt Christopher F. Santos



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Loan Proceeds Lp - actual amount received by the borrower on the origin date Lp = F Lp = F Lp = F (1

Id Fdt dt)

NOTE: 1 d is computed on F ; r is computed on P. 2 In problems involving discount interest rates, we always apply the BANKER’S RULE when the O.D. and M.D. are given. Christopher F. Santos



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Id Fdt dt)




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Id Fdt dt)




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Id Fdt dt)




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Examples 1. Find the discount interest and the proceeds of 4,000PhP due at the end of 8 months if the discount interest rate is 10 12 %. ANS. Id = 280PhP; Lp = 3720PhP 2. Find the interest charged in advance on 20,000PhP due in 210 days at a discount interest rate of 7 12 %. What is the present value of this 20,000PhP? ANS. Id = 875PhP; Lp = 19, 125PhP Christopher F. Santos



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Examples 3. If 24,000PhP is the present value of 27,500PhP due at the end of 16 months, find the 1

discount interest rate ANS. 9.55%

2

simple interest rate ANS. 10.94%

4. Find the amount due at the end of 7 months on a present value of 3,790PhP at 1

9% simple interest rate ANS. 3,988.98PhP


2

9% discount interest rate ANS. 4,000PhP



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Assignment 1

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Discount 60,000PhP due in 150 days at a discount interest rate of 8%. (Note: To discount means to find the present value, which should be more appropriately referred to as the proceeds for a given amount of money due at a future time.) Lito received 11,500PhP proceeds for a loan he applied for at a 12% discount interest rate on June 15, 2011. How much is the loan which is to be due on November 15, 2011? What is the term of the loan whose proceeds and maturity value are 67,820PhP and 80,000PhP, respectively, at a simple discount rate of 8.7%? Christopher F. Santos



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(Promissory) Note - a written promise drawn by a person or business entity (drawer/maker) to another person or business entity (drawee/payee) to pay a certain sum at a specified time and interest rate TWO TYPES: 1 Simple Interest Note - uses simple interest; face value is the principal 2 Bank Discount Note - uses discount interest; face value is the maturity value Face Value - value stated in the note Christopher F. Santos



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Example of a Simple Interest Note 10,000PhP Taft Ave, Manila January 14, 2016 Seventy-Five Days, after the above date, the undersigned promises to pay to the order of Company ABC Ten Thousand Pesos with simple interest at 12% per annum. (Sgd) Juan dela Cruz Determine the drawer, drawee, face value, simple interest rate, term, O.D. and M.D. of the note above. Christopher F. Santos



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Examples 1. What is the term of a simple interest note with a face value of 80,000PhP, a maturity value of 83,100PhP, and an interest rate of 15.5%? ANS. 0.25 years or 3 months 2. A simple interest note for 120 days at 13.8% per annum has a maturity value of 57,530PhP. What is the face value of the note? ANS. 55,000PhP Christopher F. Santos



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Example of a Bank Discount Note

70,000PhP

Manila, Philippines

Oct. 7, 2009

Three Months, after the above date, for value received with interest at 13.75% per annum discounted to maturity, the undersigned promises to pay to the order of Pasig Centennial Bank Seventy Thousand Pesos. (Sgd) Ding Javier

Determine the drawer, drawee, face value, discount interest rate, term, O.D. and M.D. of the note above. Christopher F. Santos



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Examples 1. Find the interest deducted in advance and the proceeds of a 90,000PhP bank discount note with an interest rate in advance of 18% per annum, and a term of June 4, 2011 to March 3, 2012. ANS. Id = 12, 285PhP, Lp = 77, 715PhP 2. Ted Mars signed a 10,000PhP bank discount note. If the proceeds were 8,750PhP and the term was 10 months, at what rate was the interest charged in advance? ANS. 15% Christopher F. Santos



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Discounting Notes

If the drawee of a note needs money prior to maturity date, he can sell the note at a discount to a third party, which may be a financial institution or an individual. In such case, the third party becomes the new drawee and is said to have discounted the note. The third party keeps the note until its maturity date on which the drawer pays the third party the maturity value of the note.




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Discounting Notes

The length of time from the date the note is discounted to the maturity date is called the discount period t. The amount of money that the third party pay the original drawee is the loan proceeds Lp . This is also referred to as the discounted value of the note on the date it is discounted by the third party.




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Steps in Discounting Bank Discount Notes 1 2

Determine the discount period. Compute the proceeds using the discount rate and the discount period.

Ex. Allan bought office equipment from Boy for which Allan made out a 70,000PhP bank discount note promising to pay Boy on August 29, 2010. Boy needs money on June 16, 2010 and sells the note to Charlie, who discounts it at 13.8%. Find Boy’s proceeds. ANS. 68,014.33PhP NOTE: On August 29, 2010, Charlie collects 70,000PhP from Allan. Christopher F. Santos



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Steps in Discounting Simple Interest Notes 1

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Compute the maturity value F of the note using the formula F = P(1 + rt). Determine the discount period. Compute the proceeds using the discount rate and the discount period.

Ex. Boy holds a 28,000PhP note at 12% simple interest good for 150 days. It was drawn by Allan on March 16, 2009. If interest charged in advance is 14%, how much will Boy receive if the note is encashed at a bank on June 29, 2009? ANS. 28,885.50PhP Christopher F. Santos



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Assignment 1

2

A 30,000PhP bank discount note that was to mature on August 1, 2010 was sold on May 2, 2010 at 12% discount interest. How much was the discount? What was the discounted value of the note? On August 8, 2010, Allan promised to pay Noel 8,000PhP in 45 days with simple interest at 12%. Noel, however, sold the note to Chris 9 days later at a 10% discount rate. How much did Chris pay Noel? How much did Noel earn in 9 days by having lent Allan 8,000PhP? Christopher F. Santos



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BUSANA1 Chapter1 - Simple Interest and Discount

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