 Hello and welcome to the session. In this session, first of all let us discuss the amount of NUT left unpaid. Now if the NUT is left unpaid for N years then the equivalent amount which will be paid at the end of Nth year is same as the amount the ordinary NUT certain. Therefore the amount of ordinary NUT that is A is equal to A upon I into 1 plus I whole raised to power N minus 1 the whole where A that is small A is the annual payment of each installment of NNUT of N periods the rate of interest is R% per period and I lose the interest of 1 dollar for the same period and I is equal to R upon 100. Now let us discuss what is a thinking fund. Now it is a fund that is accumulated for the purpose financial application in future designated date. Now if the periodic is required to accumulate capital A dollars to periods where interest percent fund period is the interest for the same period and I is equal to R upon 100 then capital A is equal to A upon I into 1 plus I whole raised to power N minus 1. In future 1 plus I minus 1 and this complete whole and this implies A is equal to capital A into I raised to power N minus 1 and this complete whole. An example to accumulate money from his retirement age by setting aside a certain sum of money every year which will earn him compound interest it is done by investing is created. Now a thinking fund was created for the following purposes. Child's education, second is machine replacement and third is redemption of the values. Now let us discuss endowment and scholarship. Now in this the individual may donate the money in a lump sum or number of years so that a purpose will be created from the donation to pay scholarships to bride or native students every year and such a purpose is called an endowment fund. And here the scholarship will be paid for a fixed number of years or in perpetuity that is forever and it cannot be called as a scholarship fund. Now let us illustrate it with the help of an example. Now suppose dollars per annum awarded in the bank giving an interest now if the scholarship is awarded that is in perpetuity that is forever then we have capital P is equal to A upon I. Now here A is given to us as 5000 dollars so this is equal to 5000 and I is equal to I upon 100 that is 5 upon 100 so this will be 5 upon 100 so P will be equal to 5000 over 5 into 100. Which is 100000 dollars. Now this is the amount which will have to be deposited in the lump sum to meet the liability of a payment of scholarship of 5000 dollars per annum and lastly then P will be equal to A upon I into 1 minus 1 plus I whole raised to power minus N and this complete whole which is equal to upon which is 0.05 into 1 minus 1 plus I will be equal to 1.05 minus 5 upon 0.05 into 1 minus 1 upon 1.05 whole raised to power 5 and this complete whole upon 0.05 into 1 minus 1 upon this is equal to 5000 upon 0.05 into 1 minus 0.78 whole the whole which is equal to upon 0.05 into 0.21600 dollars. Now this is the amount which will have to be deposited in the lump sum to meet the liability of a payment of a scholarship of 5000 dollars per annum for the period of 5 years. Scholarships may be paid in perpetuity so in this session you have learnt about left unpaid scholarship fund. So this concludes our session. Hope you all have enjoyed the session.