 Hello and welcome to the session. In this session, first we are going to discuss what is discount. Nowadays, producers or wholesalers of goods mark their article price greater than the cost price and then deduct a certain percentage from the marked price of their goods for a tax payment. Therefore, we can say that discount is an act of reducing the payment size of an article. We can also define it as a reduction made from the gross amount or value of something that is a reduction made from list price. Let's take an example. A dealer quoted $450 on a mobile set to a customer who will mark payment for a year but he agrees to deduct 10% on $450 that is the marked price if the buyer pays at once. The marked price of the mobile set is given as $450 and if the buyer pays at once the dealer gives him the discount of 10% on the marked price. So, this count will be equal to 10% of $450 which is equal to $10,000 into $450 that is equal to $45. So, the cash price of the mobile set will be marked price minus discount that is $450 minus $45 which is equal to $405 that is $45 is deducted here and is called the cash discount. Let's take another example. A dealer allows 5% discount on the marked price of $40 on footwear but we will be met by the footwear. Here, the marked price of the footwear is given as $40 and the dealer allows a discount of 5% on the marked price. Therefore, this count is equal to 5% of $40 which is equal to 5 upon 100 into $40 that is equal to $2. Therefore, the marked price is equal to marked price minus discount that is $40 minus $2 which is equal to $38. Now, let's discuss 2% worth and 2% discount. 2% worth of a given sum due at the end of the given period is that sum which together with its interest for the given period equals to the given sum that is present worth, interest and present worth is equal to sum due For example, we can say that a sum of $600 will amount to $654 in 2 years at 4.5% per annum which means that at 4.5% per annum rate of interest a man who has $600 now is in as good a position as a man who will be due to receive $654 in 2 years time. So, we can say that $600 is called the true present worth of $654 in 2 years time. Reckoning simple interest at 4.5% per annum we can also say that if a person has to pay $654 in 2 years time he has to pay $600 now and clear off his debt that is if he pays now then he pays $54 less than the nominal amount of the debt. This reduction of $54 is called the true discount and can be defined as the interest on the true present worth for the time which we elapsed before the debt is due to be paid. From the above discussion we can conclude that the present worth is synonymous to the principal and the bill is synonymous to the amount the true discount is simple interest. Let us now discuss as a bright formula to find interest and discount. Let p be the principal and bill is I be the interest of $1 for 1 year and b be the number of years capital I is the interest and a be the amount. So here we are going to discuss interest, discount, present worth or present value in the ordinary arrest medical sense. Now the interest on principal p for 1 year is p into I for n years the interest for principal p will become I is equal to p into n into I. This implies that amount a is equal to principal p plus interest I that is a is equal to p plus p into n into I which is equal to p into 1 plus n into I a is equal to p into 1 plus n into I which implies that p is given by a upon 1 plus n into I. Now let a be the sum of the bill p be present worth the interest of $1 for 1 year, d be true discount and m the number of years then the present worth p is given by a upon 1 plus n into I and d be true discount is equal to a minus p which is equal to a minus a upon 1 plus n into I which is equal to a plus a into n into I minus a upon 1 plus n into I which is equal to a into n into I upon 1 plus n into I therefore d is equal to a into n into I upon 1 plus n into I Let us take an example find the true present worth and true discount on $11,000 due in 15 months at simple interest 8% per annum Here we are given the value of a is equal to $11,000 and I is given as 8% per annum that is 8 upon 100 in the weekly to 15 months which is equal to 15 by 12 years Therefore d true present worth p which is given by the formula a upon 1 plus n into I is equal to a that is 11,000 upon 1 plus n that is 15 by 12 into I that is 8 by 100 which is equal to 11,000 upon 1 plus 120 upon 1200 which is equal to 11,000 upon 1 plus 1 by 10 which is equal to 11,000 upon 10 plus 1 by 10 that is equal to 11,000 upon 11 by 10 which is equal to 11,000 by 11 into 10 which is equal to 10,000 Therefore the value of true present worth p is equal to $10,000 now true discount which is given by d is equal to a minus p which is equal to a that is 11,000 minus p that is $10,000 which is equal to $1000 therefore true discount d is equal to $1000 therefore the present worth is equal to $10,000 true discount is given by $1000 Thank you for watching this video.