 Hello and welcome to the session. In this session we will discuss the compound interest formula when the number of payments, the length of time, then we use the compound interest formula because in that case the arithmetic involved in finding out the compound interest becomes quite complicated so the compound interest formula is used which saves a great deal of time and the formula is a is equal to p into 1 plus r upon 100 the whole to the power of n where just a is the amount p is the principal is the rate of interest is the time in years so this formula would be used to find out the compound interest easily consider a problem of type 1 in which we have the principal p as 6000 dollars the rate of interest are equal to 10% per annum then n that is the time is equal to 2 years so from this formula we find out the amount at the end of would be equal to a and this would be equal to p into 1 plus r upon 100 this whole to the power of n now putting the respective values of p, r and n we have the amount a equal to 6000 into 1 plus 10 upon 100 this whole to the power 2 this is equal to 6000 into 110 upon 100 into 110 upon 100 so further on solving we get the amount a is equal to 7,260 dollars this is the amount at the end of the 2 years and now the required compound interest would be equal to the amount a minus the principal p so this is equal to 7,260 dollars minus 6000 dollars and this is equal to 1260 dollars now consider the problems of type 2 when the interest is compounded half yearly in this case we take the principal p as 5000 dollars the time n equal to 1 year now as the interest is compounded half yearly so we will consider the number of half years as n so 1 year means 2 half years so this means we have n equal to 2 now we take the annual rate equal to 10% so this means the half yearly rate taken as r would be equal to 10 upon 2 that is 5% so the amount a is equal to principal that is 5000 into 1 plus r which is 5 upon 100 so we get this whole to the power n which is 2 minus we have used the compound interest formula so this is equal to 5000 into 105 upon 100 into 105 upon 100 now further on solving we get the amount a equal to 5512.50 dollars now the compound interest would be equal to the amount a minus the principal p so this is equal to 5512.50 dollars minus the principal which in this case was 5000 dollars so we have 512.50 dollars if we compound interest so this is how we can find out the compound interest when the interest is compounded half yearly next we consider the type 3 problems when the rate of interest for successive years different if suppose we have r1 the rate of interest for the first year r2 is the rate of interest for the second year r3 is the rate of interest for the third year then the amount after is given by a equal to p that is the principal into 1 plus r1 that is the rate of interest for the first year upon 100 this whole into 1 plus r2 which is the rate of interest for the second year upon 100 this whole into 1 plus the rate of interest for the third year which is r3 upon 100 the whole consider a principal p of 4000 dollars the time t be given as 2 years the rate of interest for the first year say r1 be equal to 5 percent r2 that is the rate of interest for the second year be 10 percent then the amount after 2 years be given by a is equal to the principal that is 4000 dollars into 1 plus r1 which is 5 upon 100 this whole into 1 plus r2 that is 10 upon 100 the whole this is equal to 4000 into 105 upon 100 into 110 upon 100 dollars so we further solve and we get the amount a equal to 4620 dollars that is the amount after 2 years and now the compound interest would be equal to the amount minus the principal which is equal to 4620 dollars minus the principal which is 4000 dollars and so the compound interest is equal to 620 dollars so this is how we can find out the compound interest in different cases first when we are given the principal the rate of interest and the time and the second when they given the condition that the interest is compounded half year and third when the rate of interest for successive years are different so this completes the session hope you have understood how to use the compound interest formula