 Hello and welcome to the session. In this session we discuss the following question that says a person borrowed $2,400 on 1 January 1990 and agreed to pay $400 after 2 months, $600 after 3 months and $1,800 after 11 months. In full redemption of his debt, find the rate of interest charged. Before we move on to the solution, let's discuss the formula for the equated time of payment. We consider P1, P2, P3 and so on. The different payments due after P2, P3 and so on, is respectively the zero-bait, the equated that is capital D would be equal to P1, P1 plus P2, P2 plus P3, P3 and so on. And this whole upon P1 plus P2 plus P3 plus and so on that is equal to submission PD upon submission P. This is the key idea that we use for this question. Let's proceed with the solution now. Now the date of borrow is 1 January 1990. We assume that first value be the zero-bait. That is the date of borrow is the zero-bait made for commons in which we have the due dates, the payments, that is capital P and the number of months that is small d and p multiplied by d. The first due-bait would be after two months of the date of borrow versus the date of borrow is 1 January. So after two months of 1 January is 1 March is our first due-bait and the payment to be made on 1 March would be 200 dollars. P would be 400 and d that is number of months counted from the zero-bait that is first of January would be two months and it's to be made after two months of the date of borrow. Now P multiplied by d would be 800. Next due-bait would be three months after the date of borrow. So three months after 1 January would be first April is our next due-bait and the payment to be made on this that is capital P would be 600 dollars. So in the column of capital P that is payments we would write 600. The number of months that is small d would be three since this payment is made after three months of the date of borrow. And P multiplied by d would be 1800. Next due-bait is after 11 months of the date of borrow. The first January 11 months would be 1 December. Payment to be made in this month would be 300 dollars. So we write here here small d would be 11. Now P multiplied by d is 1800 into 11 which would be 19,800. Let's find out submission P which would be equal to 2800 dollars and submission Pd is equal to 22,400. The idea we know that the equated time of payment that is capital D is equal to submission Pd upon submission P. So now the equated this is denoted by capital D is equal to submission Pd upon submission P that is equal to 22,400 upon 2800. Now these two zero cancels with these two zero and 28 is 224. So we have capital D is equal to 8 months the borrower 2800 dollars after 8 months. Now the total interest is equal to submission P minus the money borrower this would be equal to now we know submission P is 2800 dollars. So this is equal to 2800 dollars minus money borrower which was 2400 dollars just is equal to 400 dollars. Therefore we say that interest on 2400 dollars 100 dollars rate of interest charge we would find out the interest 100 dollars. This would be equal to 2400 into 100 8 months into 100 into 100 into clamp upon 8 for a year. The sense end of the rate of interest charged per annum so we would convert 8 months into year which would be 8 upon 12. Now these two zero cancels with these two zero and four six times is 24 and six two times is 12 is 8 and four times is 100. So we get this is equal to 25% or you can say the rate of interest is equal to per annum final answer. This completes the session hope you have understood the solution of this question.