 Hello and welcome to the session. In this session we will discuss compound interest. Basically compound interest is the interest calculated on the previous year's amount. The formula for the compound interest that is C i is equal to the amount A minus the principal P. Now let's discuss the formula for the amount. Now amount when the interest is compounded annually is given by A equal to P into 1 plus r upon 100 whole to the power n where we have this P is the principal, r is the rate of interest and n is the time period. And the amount when interest is compounded half yearly is given by A equal to P into 1 plus r upon 200 whole to the power 2n where r upon 2 is the half yearly rate and 2n is the number of half years. Consider the principal P given to us be rupees 18000 the rate of interest are the 10% and the time period that is n be one year. Let's find the compound interest in two cases. First when the rate of interest is compounded annually and the rate of interest compounded half yearly. In this case that is when the rate of interest is compounded annually the amount A is equal to the principal P that is 18000 into 1 plus r which is 10 upon 100 whole to the power n which is 1. On doing this calculation we get the amount A is equal to rupees 19800 that is 19800 is the amount. So from here we get the compound interest C i is equal to the amount which is rupees 19800 minus the principal which is rupees 18000 and this is equal to rupees 1800 is the compound interest to be paid. Now let's calculate the compound interest when the rate of interest is compounded half yearly for this the amount A is equal to the principal P 18000 into 1 plus r that is 10 upon 200 whole to the power 2n where 2n are the number of half years. Now the time period given to us is one year in this one year we have two half years. So in this case 2n would be equal to 2 so this whole to the power 2 this comes out to be equal to rupees 19845 that is the amount A is rupees 19845. So here we can calculate the compound interest C i is equal to the amount rupees 19845 minus rupees 18000 which is the principal. Now this is equal to rupees 1845 so this is the compound interest. Now we discuss applications of compound interest formula we have some applications where we use the formula for the calculation of amount in compound interest like the increase or decrease in population is one of the applications. Now the other application is the growth of a bacteria if the rate of growth is known then one more application is the value of an item if its price increases or decreases in the intermediate years. Discuss one problem in which we are given that the population of a city was 12000 in the year 1995 and it increased at the rate of 5% per annum we need to find the population at the end of the year 2000. Now as it is given in the question that there is 5% increase in the population every year so every new year has new population and thus we say that it is increasing in compounded form. So we can calculate the population at the end of 2000 equal to 12000 which was the population in the year 1995 into 1 plus the rate of increase of the population that is 5 upon 100 whole to the power 5 since the difference between the years 2000 and 1995 is 5 so we take here 5 here we have used the formula for the amount a equal to principal p into 1 plus the rate of interest r upon 100 whole to the power n that is the time period on doing this calculation we get the estimated population is equal to 15315 that is 15,315 is the estimated population in the year 2000. So this is how we can use the formula for the compound interest in solving some problems this completes the session hope you have understood the concept of compound interest.