Promissory Notes_simple Interest

MAT112

TOPIC 2 INTEREST 1.0

INTRODUCTION 1.1

Definition ion of interes rest : amount of money you earned (saving or investement) amount of money you pay or extra money paid ( loan or instalment purchases)

1.2 Terms involve in interest : - Inte Intere rest st ( I ): amou amount nt of mone money y ear earne ned d or or pay pay - Type Type of of Inte Interes restt (or (or activi activity ty involv involving ing intere interest) st) i) Simpl imple e Int Interes erestt : int interes erestt calc calcul ula ated ted bas based on on the the orig origin ina al principal ii) Compound Interest : interest calculated based on the frequency or how many times the interest is calculated per year iii) iii) Annu nnuity ity : inte intere res st calc calcul ula ated ted sam same as com compoun pound d inte interrest est, except saving and payment regularly or involving periodic payment iv) iv) Inst Instal alme ment nt Pur Purch chas ases es : buy buyin ing g thin things gs or or prod produc uctt by mak makin ing g instalment payment, interest divided into two i) based on original value or flat rate ii) reducing balance v) Bank Bank Disco iscoun untt : ded deduc uctt the the inte intere res st fro from m the the loa loan vi) vi) Prom Promis isso sory ry Note Notes s : type types s of loan loan,, inte intere rest st is is calc calcul ulat ated ed bas base e on Simple interest. -

15 Jan to 28 June 2006 Exact time : Jan 31 – 15 Feb Mac April May June Total days

: 16 : 28 : 31 : 30 : 31 : 28 : 164

Approximate time Jan 30 – 15 : Feb : Mac : April : May : June : Total days :

15 30 30 30 30 28 163

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Rate Rate : the the inte interes restt charg charge e depen depend d on the metho method d us used ed i) simple simple intere interest st rate rate : r ii) compound compound interest interest : i= k/m iii) annuity annuity : i = k/m iv) bank discount discount : d v) ins instal talmen mentt a) based based on origin original al method

b) reduci reducing ng

Time Time (t) (t) : the length length or dura duratio tion n of savi saving/ ng/inv invest estmen ment/l t/loan oan (alwa (always ys in in year) i) given the duration in months : t = number of months / 12 ii) given the duration in weeks : t = number of weeks / 52 iii) given the duration in days : t = number of day/(360 or 366 or 365) Rules to change days to year a) Exact Exact time time : Calcul Calculate ate the the number number of days betwe between en two date dates s usin using g exac exactt numb number er of days days in the the part partic icul ular ar months involve b) Appro pproxi xim mate tim time : Calc Calcu ulat late the the numb umber of days days between two dates using 30 days in every month c) Ordinary Ordinary Simple Simple Intere Interest st : 360 days per year year d) Exact Exact Simple Simple Interest Interest : 365 365 or 366 366 days per per year (exact (exact)) e) Banker’s Banker’s Rule : exact exact time time / ordina ordinary ry simple simple interest interest Or exact time / 360.

Princi Principal pal : i) amoun amountt of of depo deposit sit or amoun amountt of of mone money y that that we invest invest or save in the bank ii) amount of of loan or amount amount of money money that we borrow borrow from bank or anyone that charge interest i nterest

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MAT112 iii)

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2.0

the balance or the price of the product that we buy, by paying monthly or weekly (instalment)

Accumulated amount :

i) amount accumulated at the end of the period of saving/investment (your money in the bank) ii) amount a ccumulated a t the e nd of t he period of loan (you need to pay the bank)

Promissory Notes : is the notes or agreement between the payee (a person who buy the notes), maker (a person who write the notes and sell the notes to payee)

FORMULA/CALCULATION INVOLVE 2.1 -

SIMPLE INTEREST I=Prt where P = principal , r = rate , t = time (in year)

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S=P + I

or

S=P(1+rt)

where S = the accumulated amount, P = principal , r = rate , t = time (in year) -

Examples : 1) Ahmad saved RM3000 in the bank that pays 6% simple interest, for 5 years. Find the interest earn end of 5 years, and the amount in Ahmad’s account end of 5 years. i)

P = 3000, r = 0.06, t = 5 : I = P r t I = 3000 (0.06) (5) = RM 900

ii) S = P + I = 3000 + 900 = RM3900 Or S = P ( 1 + r t ) = 3000 ( 1 + 0.06 (5) ) = RM3900 2) Ahmad borrowed RM3000 in the bank that pays 6% simple interest, for 32 months. Find the amount of interest charge, and the amount Ahmad needs to pay at the end of 32 months. i)

P = 3000,

r = 0.06, t = 32/12 : I = P r t

I = 3000 (0.06) (32/12) = RM 480 iii) S = P + I = 3000 + 480 = RM3480 Or S = P ( 1 + r t ) = 3000 ( 1 + 0.06 (32/12) ) = RM3480

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MAT112 2.2

PROMISSORY NOTES

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S=P(1+rt) D = S d td H = S ( 1 – d t ) or H = S -D where S = the simple amount, P = principal, r = rate, t = time D = bank discount, d = discount rate, td = discount period, H = proceed.

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Examples:

Payee

Length of  time (period)

Date of note

Maker (borrower)

Ros received a 90-day note on 23 January 2004 from Ali with a face 1) value of RM3000, at 6% simple interest. Find Rate i)

the maturity date Start 23 Jan 2006 Jan 31 – 23 : 8 Feb : 29 Mac : 31 April : 22 Total days must be : 90 Thus maturity date is 22 April 2006

90 days 90 – 8 = 82 82 – 29 = 53 53 – 31 = 22 22 – 22 = 0

ii) the maturity value Using simple interest formula S = P(1 + rt) = 3000 ( 1 + 0.06 (90/360)) = RM3045 Ros received a 90-day note on 23 January 2004 from Ali with a face 2) value of  RM3000, at 6% simple interest. On 21 February 2004, Ros discounted the notes to the bank at 4%. i)

the maturity date Start 23 Jan 2006 Jan 31 – 23 : 8 Feb : 29 Mac : 31 April : 22 Total days must be : 90 Thus maturity date is 22 April 2006

ii)

90 days 90 – 8 = 82 82 – 29 = 53 53 – 31 = 22 22 – 22 = 0

the maturity value Using simple interest formula S = P(1 + rt) = 3000 ( 1 + 0.06 (90/360)) = RM3045 iii) the discount period Calculate the number of days starting from discount date until maturity date Start 21 February 2004 Feb 29 – 21 : 8 Mac : 31 April : 22 Total days : 60 Thus the discount period is 60 days iv) the discount Means the discount amount that the bank will charge

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MAT112 D=Sdt = 3045 ( 0.04) (60/360) = RM20.3 v) the proceed Means the amount received by Ros from the bank H=S–D = 3045 – 20.3 = RM3024.7

3.0

or H = S ( 1 – d t ) = 3045 ( 1 – (0.04)(60/360)) = RM3024.7

STEPS TO SOLVE QUESTIONS ON SIMPLE INTEREST AND PROMISSORY NOTES 3.1

Steps to solve questions on Simple interest and Promissory notes 1 )

Identify the question

type

of   Examples

How ? - Stated in the question Only simple interest involve Promissory notes, but using simple interest formula

a) Ali saved RM2300 in the bank pays 6% simple interest for 5 years. b) Isa received a 100-day note from Firdaus at 5%, with face value of RM2500 dated on 31 Mac 2005. c) Isa received a 100-day note from Firdaus at 5%, with face value of RM2500 dated on 31 Mac 2005. He sold the note to the bank at 4% on 5 May 2005.

Promissory notes, using simple interest and also bank discount (involve proceed)

2 )

Solving a 1) write the formula involve for simple interest 2) get the information from the question and substitute in the formula 3) calculate the missing value or ask by the question

3 )

S = P ( 1 + r t) P = 2300, r = 0.06 , t = 5

S = 2300 ( 1 + 0.06 (5)) = RM2990

Solving b (same as a) 1) write the formula involve for simple interest 2) get the information from the question and substitute in the formula 3) calculate the missing value or ask by the question

S = P ( 1 + r t) P = 2500, r = 0.05 , t = 100/360

S = 2500 ( 1 + 0.05 (100/360)) = RM2534.72

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MAT112 4 )

Solving c two parts)

(divided into Simple Interest S = P ( 1 + r t) P = 2500 1) involve simple interest r = 0.05 like solution above. t = 100/360 2) using bank discount formula (using the value S = 2500 (1 + of S from 1) 0.05 (100/360)) = RM2534.72 3) calculate the missing value or ask by the question

Bank Discount D = S d td H = S ( 1 – d td ) d = 0.04 S = RM2534.72 td = from 31 Mac to maturity date calculate the number of days from 31 Mac to 5 May : 35 days 100 – 35 days = 65 days td = 65/360 H = 2534.72 ( 1 – 0.04 (65/360)) = RM2516.41

4.0

EXERCISES a)

RM1500 was invested for a certain period. The simple interest rate offered was 8% per annum. If the value at the end of the period was RM1770, find the period of investment.

 b)

On 5th February 2000, Rahim opened an account in a bank by depositing RM5000. The account offered simple interest at 10.5% per annum. He closed the account on 14th June 2000. Using Banker’s Rule, find the amount he obtained. (4 marks)

c)

Aliah received 120-day promissory notes with a face value of RM3000 at 6% interest rate. The date of the note is 12 March 1996, and this note is sold to the bank on 14 May 1996 with the rate of 8%. i. Find the maturity date; ii. Find the maturity value; iii. Find the proceed; iv. Find the discount rate that is equivalent to the simple interest above.

Prepared by Cik Hamidah Ayub