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4.5 Simple Interest:
The money given by a depositor to Bank or the money given
by bank to a borrower is called ‘PRINCIPAL’
Amount. The duration for which money given by depositor to the Bank or the
duration for which money is taken on loan from bank is called ‘PERIOD or TERM’ The interest one gets from bank or
the interest charged by a Bank on a loan is normally expressed as a % for an
year. Since Banks also have to make
profit after paying for expenses ( rent
for the building, salary to its employees printing of stationary, electricity
and other expenses). Bank’s major income comes from interest charged on
loans. They also pay interest to
depositors. Thus, in order that Banks
are profitable they charge more interest on loans (around 5% more) when compared
to interest given on deposits.
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4.5 Example 1:Ram has deposited 5000Rs in State
Bank of
What does 8% interest mean to Ram? (The bank agrees to pay
8 Rupees for every 100 Rupees every year)
It is given that for Rs. 100 he gets 8 Rs per year (8%
interest)
For Rs. 5000 he gets 8*5000/100 = 400Rs per year
Since he has deposited Rs.5000, he should get Rs.400 every
year for 6 years
In all he will get Rs.2400 (=400*6) as interest in 6 years
from Bank
He will also get back his principal amount of 5000Rs at
the end of 6 years
In banking terms this method of arriving interest is
called ‘Simple Interest’
If
P = Principal amount (The sum borrowed or the sum lent)
N = Period (Term) of Deposit/loan in years
R = Rate of Interest (The interest amount on every Rs 100
for one year)
I = The interest money paid by
borrower to the money lender or to the bank for use of money (P) borrowed
A =The amount paid/payable at the end of period then(A = P+I )
For simple Interest calculation we use the formula:
Simple Interest
(SI)= (P*N*R)/100
Let us verify correctness of our interest calculation in the above example
using the above formula
Verification:
P = 5000
N= 6years
R = 8%
Substituting these values in the above formula we get
Interest = (P*N*R)/100
= (5000*6*8)/100 = 50*6*008 =2400 which is what we arrived
in the example
Since A = P+I and I = P*N*R/100
A = P+ (P*N*R)/100 = P{1+ (N*R)/100}
For easy calculation of interest, Bank employees use a table called ‘Ready Reckoner’ (Pre calculated table of interest for different amount and interest
rates) for calculating simple
interest. It is a table showing interest amount for one month or for one day
for different ‘Principal’ amounts.
Sample Ready Reckoner for interest for One Month is given
below:
Principal(Rs.) |
Rate@
4% Per
Annum |
1 |
.0033 |
2 |
.0067 |
... |
….. |
10 |
.0333 |
20 |
.0667 |
30 |
.1000 |
40 |
.1333 |
50 |
.1667 |
100 |
.3333 |
200 |
.6667 |
300 |
1.0000 |
400 |
1.3333 |
500 |
1.6667 |
1000 |
3.3333 |
... |
….. |
4.5 Problem 1: Calculate simple interest for Rs
550 at 4% for 4 months using the above Ready Reckoner
Solution :
Step 1.
550 = 500+50 (split the principal so as
to use the table easily)
Step 2: Interest for one month for Rs 500 = 1.6667
Interest for one
month for Rs.50 = .1667
Step 3 : interest for one month
for Rs 550 = 1. 8334(=1.6667+.1667)
Step 4 : interest for 4 months
= (1.8334)*4 = 7.3336
Activity : Visit a Bank and ask for a Ready Reckoner. You
will notice that Interest is tabulated
for the principal amount from Rs 1 to 9 and then from 10 in multiples of 10 up to 50 and then multiples of 100 up to 500
and then multiple 1000 up to 5000 and so
on.
Did you ever think why it is so? The reason is that any
amount can be split among small numbers appearing in the Ready Reckoner table
For example, 6047 = 5000+1000+40+7 and hence interest on
6047 is same as sum of interest on the split amounts of 5000,1000,40,7
Note:
As per the above ready Reckoner,
For Rs.100 the interest at the rate of 4% is0.3333. However, can we not calculate the
interest on 100 in another way as (Interest on Rs.1*100)=
.0033*100=.3300. Notice the difference in interest between two methods which is
.0033. This is because, the calculation of
interest is done only up to 4 decimal places and hence a rounding error.
If the amount deposited is very large, the interest difference will be huge.
Because of this reason, the person who uses Ready Reckoner has to be careful.
Let us take the case of borrower.
4.5 Problem 2: Mr. Raj borrows from State Bank
of
Solution :
In this case we have
P = 150000
R= 12
N =7
Substituting these values in the formula we get
Total interest = 150000*7*(12/100) = 1500*7*12 = 126000
Since he also pays principal loan amount at the end, his total payment to bank will be Rs
2,76,000(=1,50,000as principal +1,26,000 as Interest)
4.5 Problem 3: A sum of money amounts to Rs
3,360 at 14% Simple interest in 3 years. Find the interest on the same sum for
3 1/2 months at 6%
Solution :
In this case we have
A = 3360, R =14 and N=3
But A = P{1+
(N*R)/100}
3360 = P{1+
(3*14)/100} = p*142/100
P =
3360*100/142 = 2366
R = 6 and N = 3 1/2
months= 3.5/12 years
SI = (P*N*R)/100= {2366*(3.5/12)*6/100} = Rs. 41.41
4.5 Problem 4:
Three sisters are 5, 10 and 15 years old. Their father leaves Rs80,250 in a bank; paying 5% simple interest. If each gets the
same amount at the age of 20, find their shares at the time of father’s death.
Solution :
Since each of the sister get the amount at the age of 20 years.
Let the sister’s share be P1,P2
and P3 respectively
First sister’s share (P1) is held in the bank
for 15 years
Second sister’s share (P2) is held in the bank
for 10 years
Third sister’s share (P3) is held in the bank
for 5 years
The amount got by first sister after 15 years
= P1{1+ (N*R)/100}= P1{1+ (15*5)/100} =1.75 P1
The amount got by second sister after 10 years
= P2 {1+ (N*R)/100}= P2 {1+ (10*5)/100} =1.5 P2
The amount got by third sister after 5 years
= P3{1+ (N*R)/100}= P3{1+ (5*5)/100} =1.25 P3
Since it is given that the amount they get at the age of
20 years is same
1.75 P1=1.5 P2=1.25 P3
On simplification we get
7P1=6P2=5P3
P2 = 7/6P1
and
P3 = 7/5P1
But it is given that P1+P2+P3
= 80250
P1+7/6P1+7/5P1=
80250
I.e. (30+35+42)/30 P1= 80250
I.e. P1= 80250*30/107 = 22500
By substituting this value we find that
P2 = 7/6P1= 26250
P3 = 7/5P1= 31500
The sisters share at the time of their father’s death is
Rs 22,500, Rs26,250 and Rs,31,500.
Verify using the formula that these
deposits fetch same amount when the sisters attain the age of 20 years.
4.5 Summary of learning
No |
Points to remember |
1 |
Simple Interest (SI)= P*N*(R/100)
Where P =
Principal Amount N = Period (Term) of Deposit: R = Rate of Interest |