CHAPTER 3
SIMPLE INTEREST
Interest can be defined in tow ways.
Definition 1:
Interest is money earned when money is invested.
For example, you deposited RM1000 in a bank for a year and you find that at the end of year 1, you have RM1050 in your account. The additional amount of RM50 is the interest you earned when you invested RM1000.
Definition 2:
Interest is charge incurred when a loan or credit is obtained..
For example, you borrowed RM1000 from the same bank for a year and you paid back RM1080 at the end of that year. The additional amount of RM80 is the charge or interest you need to pay when you borrow RM1000.
Interest is the money that borrowers pay for the privilege of using someone else’s money. The amount borrowed is called the principal and when only the principal earns interest for the term of transactation, the interest due at the end of the term is called simple interest.
The amount of simple interest due at the end of the term depends on the principal (P), the length of the term (t) and the rate of interest ®.
Simple Interest Formula
Simple interest is the interest calculated on the original principal for the entire period it is borrowed or invested. It is the product of the principal multiplied by the rate and time. This may be stated as the formula
Where,
I = Simple interest
P = Principal
R = rate of the simple interest (usually given as a percent)
T = the time measured in years @ fraction there of.
Example:
RM1000 is invested for two years in a bank, earning a simple interest rate of 8% per annum. Find the simple interest earned.
I = Prt
= 1000 (0.08) (5)
= RM160
Solution
Year
Principal = RM1000
Interest for first year = 1000 X 0.08 X 1 = RM80
Simple amount = RM1080
Interest for second year = 1000 X 0.08 X 1 = RM80
Simple amount = RM1160
Interest earned = RM1160 – RM1000
= RM160
Or
I = Prt
= 1000 X 0.08 X 2
=RM160
Simple Amount Formula
The simple amount is the sum of the original principal and the interest earned. The simple amount formula is given as
Example:
RM10000 is invested for 4 years 9 months in a bank earning a simple interest rate of 10% per annum. Find the simple amount at the end of the investment period.
S = P(1 + rt)
= 10000 ( 1 + (0.1)(4.75)
= RM14750
Question
Find the simple interest and the amount at simple interest of:
a) RM400 for 5 years at 3 ½ p.a.
I = Prt
= 400 (0.035) (5)
= RM70
S = P + I
= 400 + 70
= RM470
b) RM800 for 2 years at 5% p.a
I = Prt
= 800 (0.05) (2)
= RM80
S = P + I
= 800 + 80
= RM880
Note:
When time is given in month, the time in years is found by dividing by 12.
Question
Cik Nur Irdina Darwisya borrows RM500 at 12% simple interest for 6 months. How much does she need to pay at the end of the term of the loan?.
S = P(1 + rt)
= 500 ( 1 + (0.12)(1/2)
= 500 (1.06)
= RM530
I = Prt
= 500 (0.12) (1/2)
= RM30
S = P + I
= 500 + 30
= RM530
Question
Nur Alesya Adriana invests RM5000 in an investment fund for three years. At the end of the investment period, his investment will be worth RM6125. Find the simple interest rate that is offered.
S = P(1 + rt)
6125 = 5000 ( 1 + (r)(3)
r = 7.5%
Question 1
Find
a) simple interest earned
b) simple amount
for the following investments
i) RM10,000 for 5 years at 12% per annum
ii) RM20,000 for 4 years 6 months at 11% per annum.
iii) RM15,000 for 5¼ years at 9% per annum
iv) RM7,000 for 45 months at 8% per annum
v) RM10,000 for 40 weeks at 4% per annum
Question 2
A loan RM300 will become RM333.75 after a definite period. If the loan is charged a simple interest of 7.5% per annum, find the definite period.
Question 3
Nur Irdina Darwisya invests RM10,000 in an investment fund for three years. At the end of the investment period, his investment will be worth RM12,250. Find the simple interest rate that is offered.
Answers
Question 1
i. RM6000, RM16000
ii. RM9900, RM29900
iii. RM7087.5, RM22087.5
iv. RM2100, RM9100
v. RM307.69, 10307.69
Question 2
S = P(1 + rt)
333.75 = 300 (1 + 0.075t)
1.1125 = 1 + 0.075t
0.1125 = 0.075t
1.5 = t
Question 3
S = P(1 + rt)
12250 = 10000 (1 + r3)
1.225 = 1 + 3r
0.225 = 3r
7.5% = r
Question 1
Nur Irdina Darwisya invests RM5,000 in an investment fund for six years. At the end of the investment period, his investment will be worth RM5,885. Find the simple interest rate that is offered.
Question 2
Nur Harisya Adlina borrows RM2,000 at 5% simple interest for 2 years. How much does she need to pay at the end of the term of the loan?.
Question 3
Nur Alesya Adriana borrows RM5,000 at 10% simple interest for 6 months. How much does she need to pay at the end of the term of the loan?.
Question 4
Nadiatul Hazwani invests a certain amount of money. The investment will be worth RM350 after 2 months. Find the original investment if the account offers 1.65% per annum simple interest.
Question 5
Nurin Erdiani saved RM5,000 at 8% per annum simple interest. If she withdraws RM2550 after 14 years, find the amount in the account?.
Answers
Question 1
S = P(1 + rt)
5885 = 5000 ( 1 + (r)(6)
1.177 = 1 + 6r
2.95% = r /
Question 2
S = P(1 + rt)
= 2000 ( 1 + (0.05)(2)
= 2000(1.1)
= RM2200
Question 3
S = P(1 + rt)
= 5000 ( 1 + (0.1)(6/12)
= 5000(1.05)
= RM5250
Question 4
S = P(1 + rt)
350 = P ( 1 + (0.0165)(2/12)
350 = P (1.0027499)
RM349.04 = P
Question 5
S = P(1 + rt)
= 5000 ( 1 + (0.08)(14)
= RM10600
The amount in the account = 10600 – 2550
= RM8050 /
Four Basic Concepts
i) Exact time it sis the exact number of days between two given dates
ii) Approximate time it assumes a month has 30 days in the calculation of
number of days between two given dates
iii) Exact simple interest calculated using a 365 days a year
calculated using a 366 days for a leap year.
iv) Ordinary simple interest calculated using a 360 days for a year
The length of time:
2 methods are used to determine the number of days
a. Exact time
Number of days = Nu. of the day left in the first month (+)
Nu. of the day in the following month (+)
Nu. of the day due to the maturity date
Example:
Find the exact time from January 15,1987 to 20, 1987.
January 31 – 15 = 16
February 28
Mac 20
64 days
b. Approximate time
Example:
Find the exact time from January 15, 1987 and Mac 20, 1987.
Year Month Day
1987 3 20
1987 1 15
0 2 5 ( 2X 30) + 5 = 65 days
Question 1
Find the exact time and the approximate from July 15, 1997 to October 25, 1997.
Exact time
July 31 – 15 = 16
August 28
September 30
October 25
102 days
Approximate time
Year Month Day
1997 10 25
1997 7 15
0 3 10
(3 X 30) + 10 = 100 days
Question 2
Find the exact time and the approximate from November 30, 1996 and September 9, 1997
Exact time = 31 + 31 +29 + 31 +30 + 31 + 30 + 31 + 31 + 9
= 284 days
Approximate time
Year Month Day
1992 9 9
1991 11 30
0 9 9
(9 X 30) + 9 = 279 days
Question 3
Find the exact time and the approximate from Mac 15, 1980 ro May 20, 1987.
Exact time = 1981 + 1982 + 1983 + 1984 + 1985 +1986
= (365 X 5) + 366
= 2191
= (31 – 15) + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 + 2191 + 31 + 28 + 31 + 30 + 20
= 2622 days
Approximate time
Year Month Day
1987 5 20
1990 3 15
7 2 5
= (7 X 365) + (2 X 30) + 5
= 2655 + 60 +5
= 2620 days
Exact Interest - calculated using a 365 days a year
- calculated using a 366 days for a leap year.
Ordinaray Interest - calculated using a 360 days for a year
Example:
Ahmad borrows RM5000 at 10% simple interest and has to pay back within 50 day. Find the exact interest and ordinary interest for En. Ahmad.
a. Exact Interest
I = Prt
= 5000 (0.1) (50 / 365)
= RM68.49
b. Ordinary Interest
I = Prt
= 5000 (0.1) (50 / 360)
= RM69.44
Exact time and ordinary simple interest is called Banker’s Rule. This method is mostly used by banks in U.S.A and in international business transactions but not in Malaysia. In Malaysia calculation of interest is governed by a banking rule which stated 365 day year must be used.
Introduction
There are many ways a company can raise money for working capital and expansion. It can issue new shares, borrow from banks, issued bonds or promissory notes. Promissory notes or notes in short are usually debt instruments and are issued on short-term basis.
Promissory Note
Promissory notes or notes in short are debt instruments. They can be used by anyone who wants to borrow money from or lend money to another person or party. Essentially, they are important negotiable instrument is a signed document that promises the bearer a stated sum of money at a future date or on demand. Many companies issue notes to raise money. Familiarity with the mechanics of promissory notes will certainly enhance the understanding of its role in the economy.
A promissory note is a written promise made by one person or party to repay a loan or debt on a specific future date to another person or party. Promissory notes are negotiable documents and can be of two types, interest bearing notes and non-interest bearing notes. For an interest bearing note, the rate of interest is stated on the note and is usually a simple interest rate. The main features of a promissory note are as follow.
• Marker
The maker (promisor or obligor) is the person that signs the note.
• Payee
The payee (promisee or oblige) is the person to whom the payment is to be made.
• Date of the note
The date of the note is the date on which the note is made.
• Term of the note
The term of the note is the length of time until the note is due to payment.
• Face value
The face value of the note is the amount stated on the note.
• Maturity value
The maturity value of the note is the total sum of money which the payee will receive on the maturity date. The maturity value of a non-interest bearing note is the face value while the maturity value of an interest-bearing note is the face value plus any interest that is due.
• Maturity date
The maturity date of the note is the date on which the maturity value is due.
An example of a promissory not is shown below:
Promissory note
Example
In the promissory note above
a. Who is the maker of the note
b. Who is the payee of the note?
Calculate the maturity value of the note
Solution
a. The maker is Nur Iqlima
b. The payee is Nur Elfreeda
Maturity value = Face value + interest due
= 2500 + 2500 X 0.08 X 60 ÷ 360
= RM2533.33
Example
A promissory note dated 22 February 2005 reads three months from date I promise to pay RM1000.00 with interest at 9% per annum. Find
a. The maturity date of the note
b. The maturity value of the note
Solution
a. Maturity date = 22 February 2005 + 3 months
= 22 May 2005
b. Maturity value = face value + interest due
= 1000 + (1000 X 0.09 X 3/12)
= RM1022.50
Example
The maturity value of a 60 day interest bearing promissory note is RM450. If the interest rate is 6% per annum, what is the face value of the note?.
Solution
Maturity value = face value + interest due
450 = FV + (FV X 0.06 X 2/12)
450 = FV + 0.0099999FV
450 = 1.0099999FV
RM445.54 = FV
Example
The interest on 90 day promissory note is RM46. If the interest rate is 7% per annum, find the face value of the note.
Solution
Maturity value = face value + interest due
46 = FV + (FV X 0.07 X 3/12)
46 = FV + 0.0175FV
46 = 1.0175FV
RM45.21 = FV
Example
Ali owes Ahmad RM3000 and a promissory note has been signature. He borrowed the money on April 7, 1987 and promise to pay back on July 6, 1987. Find the amount of the payment if an interest rate is 8.5% per annum.
Solution
A = RM3000
t = (30-7) + 31 +30 + 6
= 90 days
r = 8.5%
S = P(1 + rt)
= 3000 (1 + (0.085) (90/365)
= RM3062.88
Question
A promissory note dated 15 August 2005 reads two months from date, I promise to pay RM5000.00 with interest at 8% per annum
a. Find the maturity date of the note
b. Find the maturity value of the note
Question
The maturity value of a 60 day interest bearing promissory note is RM2020. If the interest rate is 6% per annum, what is the face value of the note?
Question
The interest on a 90 day promissory note is RM200. If the interest rate is 8% per annum, find the face value of the note.
Question
In the promissory note above
a. Who is the maker of the note
b. Who is the payee of the note?
c. What is the maturity value of the note?
SIMPLE DISCOUNT
• It is common for lenders, such as banks and financial institutions to deduct the interest charge in advance for short-term loans.
• This charge is called bank discount or interest in advance.
• The net amount received by the borrower is called the proceeds.
• For example, assume a person wants to borrow RM1000 for a year from a lender who charges a 12% discount rate.
• The lender will take RM1000 X 12% X 1 = RM120 as interest in advance and the man will receive RM880 as proceeds.
• It must be noted that the man who borrows RM1000 will have to pay RM1000 at the end of the year.
• It is different if the lender charges a 12% simple interest rate.
• In such a case, the man who borrows RM1000 will receive RM1000 but has to pay back more than RM1000 at the end of one year.
• Bank discount is computed in much the same way as simple interest except that it is based on the final amount (to be paid back) or maturity value.
• Formula
D = Sdt
Where D = bank discount
S = amount of maturity date
d = discount rate
t = term of discount in years
• The proceeds, P, are computed as follows
Bank proceed = maturity value – bank discount
P = S – D
P = S – Sdt
Question
Elmira borrows RM8000 for three months from a lender who charges a discount rate of 10%. Find
a. The discount
b. The proceeds
Question
If Tong needs RM4000 now, how much should he borrow from his bank for 1 ½ years at a 12% bank discount rate?
Question
Find the bank discount and proceeds of the following loans.
a. RM5000 for 30 days at 5%.
b. RM2800 for 60 days at 3%
c. RM4000 for three months at 2.5%
d. RM3500 from 15 July to 14 August of the same year at 6%
e. RM8000 for 20 weeks at 4%
Question
a. D = Sdt
= 8000 X 0.1 X 0.25
= RM200
b. P = S – D
= 8000 – 200
= RM7800
Question
P = S(1 – dt)
4000 = S (1 – (0.12) (1.5)
RM4878.05 = S
Answers
Find the bank discount and proceeds of the following loans.
a) RM5000 for 30 days at 5%. RM20.83, RM4979.17
b) RM2800 for 60 days at 3% RM14, RM2786
c) RM4000 for three months at 2.5% RM25, RM3975
d) RM3500 from 15 July to 14 August of the same year at 6% RM18, RM3482
e) RM8000 for 20 weeks at 4% RM123.07, RM7876.92
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