 Hello and welcome to the session. In this session, we are going to discuss the following question. The question says that, on what sum of money will the difference between simple interest and compound interest for 2 years at 5% per annum will be equal to $25? Let us review some of the formulas that we will use to solve this question. The compound interest law is amount is equal to P into 1 plus r upon 100 raise to power n, where P is equal to the principal, r is equal to the rate of interest, n is equal to the time in years. Also, compound interest is equal to amount minus principal. We also know that simple interest is equal to P into r into t upon 100, where P is the principal, r is the rate of interest and t is the time in years. With this key idea, we shall proceed with the solution. According to the question, we need to find the principal that is the sum of money when the difference between the simple interest and the compound interest for 2 years at 5% per annum is equal to $25. Let the principal that is the sum of money to be calculated be equal to P. We know compound interest is equal to amount minus principal as amount is equal to P into 1 plus r upon 100 raise to power n. So here, compound interest is equal to P into 1 plus r upon 100 raise to power n minus principal. So this is equal to P into 1 plus 5 upon 100 raise to power 2 minus P. This is equal to P into 1 plus 1 upon 20 raise to power 2 minus P. That is equal to P into 20 plus 1 upon 20 whole raise to power 2 minus P which is equal to P into 21 upon 20 raise to power 2 minus P. This is equal to P into 441 upon 400 minus P. Taking the LCM, we have 441 P minus 400 P upon 400 which is equal to 41 P upon 400. So here we have calculated the compound interest in terms of P. Now let us calculate the simple interest in terms of P. We know simple interest is equal to P into r into t upon 100. So putting the values, simple interest is equal to P into 5 into 2 upon 100 that is equal to 10 P upon 100 which is equal to P by 10. So now simple interest in terms of P is equal to P by 10. It is given in the question that the difference between compound interest and simple interest is equal to 25 dollars. So if we put the values of compound interest and simple interest in terms of P in this equation, we can find the value of P. On putting these values, we have 41 P upon 400 minus P upon 10 is equal to 25. Taking the LCM, we have 41 P minus 40 P upon 400 is equal to 25. This implies P upon 400 is equal to 25 that is P is equal to 10,000 dollars. So the required sum of money is equal to 10,000 dollars which is our answer. This completes our session. Hope you enjoyed the session.