Core capital is the capital required to sustain the lifestyle.
Now, for upcoming year amount needed as core capital is given as $128,750
so, for year 2 real core capital required will be 128,750*1.03 = 132612.5
Now, this amount needs to be adjusted based on their combined probability of survival for year 2.
Combined probability of survival for year 2 = 0.7644 +0.8244 – 0.7644*0.8244 = 0.9586
so, adjusted core capital = 0.9586*132612.5 = $ 127,122.34
Now, when I did this question initially I did it upto here, but when I checked the solution they also did PV of this amount I think which I think is fair as core capital needs to estimated today for year 2, so PV nikalna padega.
so, real core capital needed today for year 2 = 127122.34 / (1.04)^2 = $117,531.7516
Core capital is the capital required to sustain the lifestyle.
Now, for upcoming year amount needed as core capital is given as $128,750
so, for year 2 real core capital required will be 128,750*1.03 = 132612.5
Now, this amount needs to be adjusted based on their combined probability of survival for year 2.
Combined probability of survival for year 2 = 0.7644 +0.8244 – 0.7644*0.8244 = 0.9586
so, adjusted core capital = 0.9586*132612.5 = $ 127,122.34
Now, when I did this question initially I did it upto here, but when I checked the solution they also did PV of this amount I think which I think is fair as core capital needs to estimated today for year 2, so PV nikalna padega.
so, real core capital needed today for year 2 = 127122.34 / (1.04)^2 = $117,531.7516