I assume you have studied simple interest in school. Now, let us recall that. The interest of principle P in time T years with of interest R was;
We don't add interest in principle while calculating simple interest. If we add interest in principle so as to make new principle on a routine basis, this is called compound interest.
If we add interest after one year as routine then;
after one year;
A = P+ I = P + PR/100 = P(1+R/100)
This is new principle now;
after two years;
A = P(1+R/100) + P(1+R/100)*R/100 = P(1+R/100)(1 + R/100) = P(1+R/100)^2
after three years;
A = P(1+R/100)^2 + P(1+R/100)^2 R/100 = P(1+R/100)^2( 1+ R/100) = P(1+R/100)^3
generalizing this;
A = P(1+R/100)^T for T years.
This result is compounded once a year. If we compounded n times in a year then more generalized result is;
A =P(1+ R/100 n)^nT
Example:
Hari takes a loan of $1,000 to buy a used truck at the rate of 5 % simple Interest. He paid total amount after 5 years. How much did he pay if
i. Interest was simple
ii. Interest was compounded yearly:
Solution:
principle = $ 1000
time = 5 years
Rate = 5 %
simple interest(SI) = PTR/100 = 100055/100 = $ 250
Amount(A1) = 1000 + 250 = $ 1250
compound amount = P(1 +r/100)^T = 1000(1+5/100)^5 = $ 1276.281
compound interest = 1276.281-1000 = $ 276.281
Since interest is added in principle, compound interest is greater than simple interest. For one year; compound interest yearly us equal to simple interest.