 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that the difference between the simple and compound interest on a certain sum of money for 2 years at 5% per annum is 401 dollars. Find the sum. We know that 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, p is equal to time. Also the compound interest formula is amount a is equal to p into 1 plus r upon 100 raise to power n. With this key idea let us proceed with the solution. According to the question the difference between the simple and compound interest on a certain sum of money is 401 dollars for 2 years at 5% per annum. We need to find the sum of money. We are given the time is equal to 2 years, rate of interest r is equal to 5% per annum. Let the sum of money be 1 dollar. Then the simple interest on 1 dollar for 2 years 5% per annum is equal to 1 into 2 into 5 upon 100 dollars which is equal to 10 upon 100 dollars that is 1 by 10 dollars. So the amount after 2 years on 1 dollar will be equal to 1 into 1 plus 5 upon 100 raise to power 2 dollars which is equal to 105 upon 100 raise to power 2 dollars that is equal to 21 upon 20 raise to power 2 dollars which can also be written as 21 into 21 upon 20 into 20 dollars that is equal to 441 upon 400 dollars. As we have calculated the simple interest as 1 by 10 dollars and the amount on compound interest as 441 upon 400 dollars. So the difference between compound interest and simple interest is equal to 441 upon 400 minus 1 upon 10 dollars which is equal to 441 minus 40 upon 400 dollars that is 401 upon 400 dollars. So if sum is 1 dollar difference between compound interest and simple interest is equal to 401 upon 400 dollars. This implies if difference is 401 dollars then sum is equal to 400 upon 401 into 401 which is equal to 400 dollars. Hence the sum of money is equal to 400 dollars which is our answer. This completes our session. Hope you enjoyed this session.