SIMPLE INTEREST

CHAPTER 2

AZLINA BINTI JUMADI@FSKM

MAT112 BUSINESS MATHEMATICS

IntroductionSimple interest formula Exact simple interestOrdinary simple interestPresent value of a debt

CONTENTS

Simple interest is the interest due at the end of a term.

In simple interest transaction, only principle (original value) will earn the interest. The principal can be the amount of money deposited in an account or the amount of money borrowed.

The amount of interest due at the end of a term depends on the principal, the length of the term and the rate of interest.

The rate is given in percent and often as annual rate.

The time is measured in years or a fraction of a year.

INTRODUCTON

The formula to find the interest (I) due at interest rate (r%) for a principal (P) for a length of t years is

In calculation, r% is converted to decimal number.

When the time is given in months, then

t =

For the time given in days, we will discuss it later.

SIMPLE INTEREST FORMULA

number of month 12

I = Prt

The future value (S) is the total amount received or due at the end of the term.i.e:

S = P + I = P + Prt

SIMPLE INTEREST FORMULA

S = P(1 + rt)

Find the interest on RM 2535.00 if the rate is 5.5 % for

3 years ?

Solution:

P = 2535, r = 5.5 % = 0.055, t = 3

Therefore, interest, I:I = Prt

= 2535 (0.055)(3) = 418.28

EXAMPLE 1 :

Mr . Raju borrowed RM4560.00 from a lender. He was

charged simple interest at 8.5%. If he wanted to settle

his debt in 4½ years, how much will he be paying the

lender?

Solution:

EXAMPLE 2 :

1) Pn. Sarina deposited RM10050.00 in an account that pay 7% simple interest for 8 months. How much will she earn at the end of the term? Ans : 10519.00

2) Leon invests RM8080.00 in a certain trust fund for 6.5 years. At the end of the investment period, his total investment will amount to RM13500.00. find the simple interest rate that was offered. Ans: 10.32%

3) How long must one deposit a sum of RM350 for it to double itself if the simple interest rate offered is 9%. Ans: 11.11 years

4) How much money is needed to be invested for 4 years in a finance company that pays simple interest 7% per annum in order to get the accumulated amount RM5555.00 at the end of the term. Ans: RM4339.84

EXERCISES:

(time given in days)

Exact interest is calculated based on 365 days a year, and for a leap year, using 366 days.

Ordinary interest is calculated using a 360 days a year. It is using an approximation that each month having 30 days. This is to simplify computing and of course it increases the amount of interest due to the lender.

EXACT SIMPLE INTEREST, ORDINARY SIMPLE INTEREST

Find the exact and ordinary simple interest on RM2000

for 50 days at 5% per annum.

SOLUTION:

EXAMPLE 3 :

When dates are given, the number of days between the

two dates is calculated in two ways. Those two ways are

exact time and approximate time.

Exact time, as the name suggested, is the exact number of days as in the calendar between two dates given.

Approximate time is found by assuming each month is 30 days flat.

It is customary to include one either the beginning or

maturity dates only.

Find the exact and approximate time from May 20, 2001

to August 28, 2001.

SOLUTION:

EXAMPLE 4 :

Find the exact and approximate time from 5 February

2000 to 30 May 2000.

SOLUTION:

EXAMPLE 5 :

Using the exact time, find the due date for 100 days from

6 May 2002.

SOLUTION:

EXAMPLE 6 :

1) Find the initial date if the duration of approximate time 75 days ends on 25 September 2001. Ans : July 10, 2001

2) Find the exact and approximate time from September 15, 2002 to february 3, 2003.Ans : exact time : 141 days

approximate time : 138 days

EXERCISES:

Since there are two ways of computing interest and two ways of calculating time, there are four distinct methods for computing interest on short-term loans or deposits.

They are:Exact time exact simple interestExact time ordinary simple interestApproximate time exact simple interestApproximate time ordinary simple interest

NOTED…

Find the exact and ordinary simple interest on RM 2500

at 7% from April 2002 to July 1, 2002 usinga) exact time b) approximate time

SOLUTION:

EXAMPLE 7 :

Of the four ways to compute simple interest, the most popular is that of ordinary interest for the exact number of days.

It is popularly known as the Banker’s rule.Of the four methods, this yields the

maximum interest in any transaction.NOTE : Unless otherwise stated, we will use

the Banker’s Rule in computing interest problems.

1) Find the ordinary simple rate for a loan worth RM1500 whose interest is RM300 for a period of 330 days. Ans : 21.82%

2) Ali borrowed RM4500 on 4 April 2000 from a loan shark that charge 6.5% simple interest and promised to settle his debt on 8 November 2000. Find using Banker’s Rule the amount he has to pay?Ans : RM 4677.13

EXERCISES:

The value of a debt at some time before the due date is called present value of the debt on that date. It is best illustrated on the time line.

We obtain the formula from the future value formula

Solving for P, we have

PRESENT VALUE OF A DEBT

0 t

present value maturity value

S = P(1 + rt)

P = S 1

+rt

Find the present value at 7% simple interest of RM1500

due in 10 months.

SOLUTION:

EXAMPLE 8 :

Mr. X promised to pay his debt with interest amounted

to RM 3500 in 3 years’ time. If the charge is 7%, find the

amount he borrowed?

SOLUTION:

EXAMPLE 9 :

1) On 5 July 2000, Miss Ching borrowed a sum of money from a finance company for her daughter’s education. She promised to pay back the loan in 150 days. The finance company charges her 5% simple interest. If the total amount she has to pay is RM 8900, find

a) the due date if time is exact. Ans: December 2, 2000

b) the interest paid if Bankers’ Rule is used. Ans: RM 181.63

2) Three years ago, a sum of money was deposited in a bank that pays interest at 8% simple interest. Today, the money has accumulated to RM 10000. Find

a) the present value of the deposit Ans: RM 8064.52

b) how many more years should the money be left in the

bank to accumulate it to RM 25000. Ans: 23¼ years

3) 125 days after borrowing a sum of money, X pays back exactly 990.85. How much was borrowed if the payment includes principal and ordinary simple interest rate at 8.5%? Ans: RM 962.44

EXERCISES:

TUTORIAL 2(PAST YEAR QUESTIONS)

SET A

(PAST YEAR QUESTIONS)SET B