Interest
Interest is money paid to the lender by the
borrower for using the money for a specified period of time. Various terms and
their general representation are as follows: .
(a) PRINCIPAL : The
original sum borrowed = P
(b) TIME
: Time for which money is borrowed = T. (T is
expressed in number of periods, which is normally one year) .
(c) RATE
OF INTEREST : Rate at which interest is calculated on the original sum =
R
(d)
AMOUNT : Sum of Principal and Interest = A
Simple Interest
Wiien interest is calculated every year (or
every time period) on the original principal, i.e., the sum at the beginning of
first year, such interest is called Simple Interest. here, year after year,
even though the interest gets accumulated and is due to the lender, this
accumulated interest is not taken into account for the purpose of calculating
interest for later years. .
Simple Interest = 
, where P,T,R are as explained above.
Total Amount A = P + , = P 
Compound interest
In Compound Interest, the interest is added
to the principal at the end of each period to arrive at the new principal for
the next period. .
In other words, the amount at the end of
first year (or period) will become the principal for the second year (or period);
the amount at the end of second period becomes the principal for the third
period and so on. .
If P denotes the principal at the beginning
of year 1, then,
P at the beginning of year 2 = P 
P at the beginning of year 3 = P 
P at the beginning of year (n + 1) = P 
Compound interest = A - P
Worked out examples
Example.1
What is
the simple interest on Rs.20000 at 18% p.a. for a period of two years?.
Solution
S.I. = where P is principal,
T is time period and
R is rate of interest. .
Here P = Rs.20000, T = 2 years and R = 18%
p.a. .
\ S.I. = 
= Rs.7200
Example.2
What sum
of money will yield a simple interest of Rs.7200 in four years at 12% p.a.? .
Solution
S.I =
As S.I. = Rs.7200, we have 7200 = 
&⇒ P = 
= Rs.15000
Example.3
In how many years a sum becomes six times
itself at 20% p.a. simple interest? .
Solution
Let the
principal be Rs.P then Amount = Rs.6P .
So, interest = 6P - P = Rs.5P .
As S.I = , 5P = 
T = 25 years. .
example.4
What sum
of money amounts to Rs.5800 in three years at 15% p.a. simple interest? .
solution
Amount =
Principal + Interest
5800 = P + 
5800 = P + 0.45P .
5800 = P(1 + 0.45) .
P = 
= Rs.4000
Example.5
What is the compound interest on Rs.1400 at
20% p.a. for a period of two years compounded annually? .
Solution
A = P, where A is amount, P is principal, R is rate of interest and n
is number of years.
Here P = Rs.1400, R = 20%, n = 2 years. .
A = 1400
, A = 1400
A = 
= Rs.2016
Compound interest = 2016 - 1400 = Rs.616 .
