hello friends, welcome to this session, let’s see introduction to compound interest, in previous session we saw simple interest so what is the difference between simple interest and compound interest, in simple interest the principal remains constant and interest also remain constant over the years but in compound interest every time interest will get added to the principal giving rise to increase interest every year let’s see how, this is my initial principal P so in Year 1, I will earn the interest of R percent of P that is my principal amount to get me the first amount that is A1 as P + r% of P, i can write that has P (1 + r/100) now what will happen in year 2, very very interesting, for year 2 the amount in my first year will become principal of my 2nd year and now I will earn interest on that amount as r% of A1 and I can write A2= A1+r% of A1 or in terms of P I can write P (1+r/100) raised to 2 and this I can now right for A3 and A4 also in year 3 what will happen A3 will be A2+r% of A2 or P(1+r/100)cube similarly for A4 the amount in my 3rd year will happen to be principal for my 4th year to give rise to the equation A 4 is equal to P(1 + r/100) raise to 4, do you realise every year my interest is getting added to the principal giving rise to increase interest every year, if I generalizes this amount in any nth year will be P(1 + r/100) raise to N and 1 more interesting phenomenon, amount and interest are changing geometrical in simple interest yes it was linear here it is in geometry proportion with the ratio same that is 1+r/100 so in any two successive amounts the ratio will always be same that is 1 + r/100 let’s go ahead, now what is this n this is number of years, no this is my time period 1, time period 2, time period 3 and 4 so n will always represent the number of compounding time periods and it is not going to be number of years very very important point to remember let’s go ahead let’s take a simple example.