it will cost 75000 per year to keep my mother in an assisted

it will cost $75000 per year to keep my mother in an assisted living home. no one knows offcourse such arrangement might be for. i will assume 10 years after she enters the home. Further let\'s assume she can live on her own home for 5 more years. she can sell her home for $320,000 in 5 years. How much money do i need to put aside today in lump so that she will be able to stay in assisted living for 10 years starting 5 years from today. assume i=8%

Solution

Lets assume we are 5 years ahead where your mother has sold her house for $320,000 and planning to move into assisted living house. In that house she will stay for 10 more years

then Present worth of cost needed to stay in assisted house equals to

Present Worth is calcultaed by discouting each cost term for an example if Cash Flow \"Z\" is assumed to be earned after \"t\" years then Present worth of \"Z\" is Z/(1+r)^t for given r

=75000/(1.08)^10+75000/(1.08)^9+75000/(1.08)^7+75000/(1.08)^6+75000/(1.08)^5+75000/(1.08)^4+75000/(1.08)^3+75000/(1.08)^2+75000/(1.08)^1

=$462735.93

We need $462,735.93-$320,000=$142,735.93 to have in account at that time that is 5 years from now

We should keep $142,735.93/(1.08)^5 in bank deposit

Answer is $97143.68