 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that A man borrows $4000 at 10% compound interest per annum. Interest payable every 6 months. He pays back $1000 at the end of every 6 months. Calculate the third payment he has to make at the end of 1.5 years in order to clear the entire loan. Now we know that simple interest is equal to P into R into T upon 100 where P is equal to the principal is equal to the rate of interest and T is equal to time. Also amount is equal to principal plus interest. With this key idea let us proceed with the solution. According to the question we have to calculate the third payment that the man has to make at the end of 1.5 years in order to clear the entire loan where the man borrows $4000 at 10% compound interest per annum and he pays back $1000 at the end of every 6 months. So here we are given the principal P is equal to $4000. The time is 1.5 years which is equal to 2 into 3 by 2 half years that is 3 half years. The rate of interest is equal to 10% per annum. So as the time is 3 half years therefore we will calculate the interest for 3 periods of 6 months each. So the principal for the first 6 months will be equal to $4000. As we know simple interest is equal to P into R into T upon 100. Therefore interest for the first 6 months is equal to $4000 into 1 by 2 into 10 upon $100 which will be equal to $200. This implies the amount after first 6 months is equal to $4000 plus $200 which is equal to $4200. Now the loan paid back 6 months is equal to $1000. So we subtract this amount from the amount paid after 6 months. We have $4200 minus $1000 which is equal to $3200. So the principal for in period of 6 months is equal to $3200. Therefore the interest for the second period of 6 months is equal to $3200 into 1 by 2 into 10 upon $100 which will be equal to $160. So the amount to be paid back for the second period of 6 months is equal to $3200 plus $160. That is equal to $3360. Again the loan paid back to 6 months is equal to $1000. So we again subtract this amount from the amount to be paid back after the second period of 6 months. And we will have $3360 minus $1000 which is equal to $2360. So now the principal for the third period of 6 months is equal to $2360 which implies the interest for the third period of 6 months is equal to $2360 into 1 by 2 into 10 upon $100. That is equal to $118. So the amount after third period of 6 months is equal to $2360 plus $118 which is equal to $2478. Therefore the amount he has to pay after 1.5 years to clear his loan is equal to $2478 which is our answer. This completes our session. Hope you enjoyed the session.