Name 3 30 pointsl figure it will cost 75000 per year to kee

Name 3. (30 points)l figure it will cost $ 75,000 per year to keep my mother in an assisted living home. No one knows of course, how long such an arrangement might be for. I will assume 10 years after she enters the home. Further, lets assume she can live on her own at home for more years. (ie no assisted living costs). She can sell her home for $ 320,000 in 5 years. How much money (f any) do I need to put aside today in a lump sum so that she will be able to stay in the assisted living for 10 years starting 5 years from today. (remember she will get $ 320,000 in 5 years as well when she sells the house.) Assume 1-8%.

Solution

ans:

since she can live arrange for her living cost for 5 years , I will only have to arrange for 5 years of her living cost i.e. 75000 * 5 = $375000 but since she can sell the home for for 320000 , I will have to arrange for only 375000 - 320000 = $ 55,000 in lump sum

F.V = P ( 1+r)^T

where F.V = future value amount

P = principal amount

r = rate of interest

T = time peroid

now,

55,000 = P ( 1+0.08)⁵

=> 55000 = P (1.4693280768)

=> P = $ 37432.0758369

HENCE, he should put aside $37,432.0758369 today