 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that, find the present worth that will produce $50 at an interest of 5.5% per annum in 2 years also find the true discount. We know that a is equal to p into 1 plus n into i and g is equal to a minus p where a is the sum of the bill p is the present worth and is the number of years i is the interest of $1 for one year if the true discount with this key idea let us proceed with the solution. Here we need to find the present worth that will produce $80 at an interest of 5.5% per annum in 2 years time. Here the value of a is given as $80 is equal to 2 years and the value of i is given as 5.5% per annum that is equal to 11 by 200 and from the key idea we know that a is equal to p into 1 plus n into i therefore we have 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 which is equal to a that is 80 upon 1 plus n into i that is 2 into 11 upon 200 which is equal to 80 upon 1 plus 11 upon 100 that is 80 upon 100 plus 11 by 100 which is equal to 80 upon 111 by 100 that is equal to 8000 by 111 which is equal to 72.07 so the value of present worth p is equal to 72.07 dollars and we know that the true discount b is given by a minus p so we have 2 discount d which is given by a minus p is equal to a that is 80 dollars minus p that is 72.07 dollars which is equal to 7.93 dollars hence the present worth is given by 72.07 dollars and the true discount 7.93 dollars this is the detailed session hope you enjoyed this session