Provide a full justification for each part a,b, and c. Thulasi owns a savings account which compounds interest annually at a rate of4% per year. She wishes to invest a lump sum $L into the account today so that every year, she can withdraw $100 from itto give to her grandson as a birthday gift. We assume that her grandson was born yesterday and that she has already given him his first present.Let An= account balance exactly n years from now. (a)(4 points) Find a non-recursive expression for Anas a function ofn and L. (b)(3 points) What is the minimum value ofL that ensures that every year for the next 40 years Thulasi can withdraw $100 from her account? Round your answer to two decimal places, (c)(3 points) What is the minimum value ofL that ensures that $100 can be withdrawn from Thulasi's account on her grandson's birthday every year for "the rest of eternity"? Round your answer to two decimal places, if needed.