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.

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}
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 P_{1},P_{2} and P_{3}
respectively
First sister’s share (P_{1}) is held in the
bank for 15 years
Second sister’s share (P_{2}) is held in
the bank for 10 years
Third sister’s share (P_{3}) is held in the bank for 5 years_{}
The amount got by first sister after 15 years
= P_{1}{1+ (N*R)/100}= P_{1}{1+ (15*5)/100} =1.75 P_{1}
The amount got by second sister after 10 years
= P_{2} {1+ (N*R)/100}= P_{2} {1+ (10*5)/100} =1.5 P_{2}
The amount got by third sister after 5 years
= P_{3}{1+ (N*R)/100}= P_{3}{1+ (5*5)/100} =1.25 P_{3}
Since it is given that the amount they get at the
age of 20 years is same
1.75 P_{1}=1.5 P_{2}=1.25 P_{3}
On simplification we get
7P_{1}=6P_{2}=5P_{3}
_{} P_{2 }= 7/6P_{1}
and P_{3 }= 7/5P_{1}
But it is given that P_{1}+P_{2}+P_{3}
= 80250
_{} P_{1}+7/6P_{1}+7/5P_{1}=
80250
I.e. (30+35+42)/30 P_{1}= 80250
I.e. P_{1}= 80250*30/107 = 22500
By substituting this value we find that
P_{2 }= 7/6P_{1}= 26250
P_{3 }= 7/5P_{1}= 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 