 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that a sum lent on compound interest becomes $4,220 in two years and $4,642 in three years. Find the sum. Simple interest is equal to P into R into T upon 100 where P is equal to the principal, R is equal to the rate of interest, T is equal to time. Also by the compound interest formula amount A is equal to P into 1 plus R upon 100 raised to power N. With this key idea let us proceed with the solution. According to the question we have to find the sum of money that is lent on compound interest which becomes $4,220 in two years and $4,642 in three years. So the amount given in three years is equal to $4,642 and the amount in two years is equal to $4,220. As we know the interest will be the difference in the amounts for two consecutive years. So interest for third year is equal to $4,642 minus $4,220 which is equal to $422. Since the amount for a particular year is the principal for next year therefore amount for two years is equal to principal for the third year which implies principal for third year is equal to $4,220 and the interest for third year is equal to $422. As we know simple interest is equal to P into R into T upon 100 therefore $422 is equal to $4,220 into R into 1 upon 100 where R is equal to the rate of interest per annum which we have to find. So this implies R is equal to $422 into 10 upon 422 which is equal to 10. So R is equal to 10% per annum. Now as we know amount A is equal to P into 1 plus R upon 100 raise to power N therefore $4,220 is equal to P into 1 plus 10 upon 100 raise to power 2 where $4,220 is the amount after two years 10% per annum is the rate of interest P is equal to the principal or the sum of money lent which we have to find. So $4,220 is equal to P into 1 plus 1 by 10 raise to power 2 which can be written as $4,220 is equal to P into 10 plus 1 upon 10 raise to power 2 which is equal to P into 11 upon 10 raise to power 2. This implies $4,220 is equal to P into 11 by 10 into 11 by 10 which implies P is equal to $4,220 into 10 into 10 upon 11 into 11 which implies P is equal to $4,220 into 100 upon 121 which implies P is equal to $3,487.60. Hence the sum of money lent is equal to $3,487.60 which is our answer. This completes our session hope you enjoyed the session.