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What is simple interest and compound interest?

The interest rate is calculated after considering the inflation rate, risk on that investment etc.
There are two types of interest:-
  1. Simple interest
  2. Compound interest
1. Simple interest is that interest which is earn on principal (borrowed) amount. It is calculated on original amount invested or borrowed for specified period. Formula to calculate simple interest (SI) is as follow:
                 SI=P*R*T 
Where,
P=the principal amount which is borrowed or invested.
R=the rate of interest which is charged on principal amount borrowed or invested.
T=the time period for which principal amount borrowed or invested.

For example - If a bank charge 5% p.a interest on Rs 20,000 for 5 ½ year. Then simple interest is calculated as:
SI=P*R*T
SI = 20000*5         (5+6)       
        ----------   *    ------ 
               100            12               
=500*11  
= 5500
With the help of it you can calculate interest          on loan, interest on investment and added the        principal amount with the interest you will get total amount paid to bank. And the formula is-
                         A=P+ (PRT)



Where,
A=total amount paid or receive on loan or investment
P=principal (borrowed or invested) amount.

2.Compound interest is an interest which is added to the principal amount to earn further interest on it. It is used to calculate total loan amount, amount received after investment etc.
Compound interest calculated by following ways:
a) Compounded annually
b)Compounded half yearly
c)Compounded quarterly
d)Compounded monthly
e)Compounded continuously

Formulae to calculate compound interest:-
Compounded annually
Compounded half yearly
Compounded quarterly
Compounded monthly
Compounded continuously
Formulae
A=P(1+r/100)t
A=P(1+r/100*n)t*n
A=P(1+r/100*n)t*n
A=P(1+r/100*n)t*n
A=P*e r*t
N (Value)
---------
2
4
12


Where,
A = the total amount received or paid.                                                                                                 
P  = the principal amount which is borrowed or invested.
n  = the rate of interest on principal amount (borrowed or invested).
t   = the time period for which principal amount borrowed or invested.
n  = number of periods interest added to the principal.
e  = the scientific constant which is equivalent to 2.718281828

a). Compounded annually:
 Example: Ravi has recently open saving  a/c in bank with Rs 25000 and bank charged 7% per annum interest  compounded annually for 2 years. Find out compound interest?
A=P (1+r/100) t
   =25000(1+7/100) 2
   =25000(107/100) 2
A=28622.5
Compound interest (CI) = amount (A)-principal (P)
                                          =28622.5-25000=3622.5   
         
b). Compounded half yearly:
 Example: Ravi has opened saving a/c in 1st January with Rs 25000 and bank charged 7% per annum interest compounded half yearly and he deposited Rs. 2500 per month from March. Find out the total amount in his a/c after 3 years.
A=P (1+r/n) n*t
=50000(1+0.07/2) 2*1 + 55000(1+0.07/2) 2*2
=53561.25 + 63113.76
=116675.01   
                                                                                                      
c). Compounded quarterly-
Example: Mr. Jai has taken a loan from bank of Rs.200000 and bank charges 8% per annum interest compounded quarterly for 4 years. Calculate amount paid after 4 years.
A=P (1+r/n) n*t
=200000(1+0.08/4) 4*4
=200000(1.02) 16
=274557.14

d). Compounded monthly-
Example:Ms. Nisha has invested Rs.30000 in National Saving Certificate (NSC) for 5 years and earns 8 % per annum interest compounded monthly. Find out the maturity amount.
A=P (1+r/n) n*t
= 30000(1+0.08/12) 12*5
=30000(1.0066) 60
=44695.38

e). Compounded continuously-
Example: Mr. Sharma has taken a home loan of Rs.10, 96,000 and bank charges 6% interest compounded continuously. Find the total amount paid by Mr. Sharma after 8 years to bank.
A=P*e r*t
=1096000*e 0.06*8
=1771217.54
                         
Calculations of Simple interest and Compound Interest in excel:

Simple interest:
A
B
1
Principal
25000
2
rate
8%
3
N
3
4
Simple interest
6000

B4 cell: “=B1*B2*B3”

Compound Interest:
A
B
1
Principal
25000
2
rate
8%
3
N
3
4
Compound interest
25060.05
                   
B4 cell: "=B1*(1+(B2/100))^B3





















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