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// calculation from article

pmt = 80000
base = 2*10^6 = 2000000
pmt/base= 0.04
i = 4/100= 0.04

// this reflects a perpetuity (forever money that can be passed from generation to generation)
// but pensions stop when you die
// so lets calculate the present value based on average life expectancy, at the given interest rate

// Early Retirement, Average Lifespan
age_retirement = 55
age_death = 75
yrs = age_death - age_retirement = 20
pv = pmt*(1-(1+i)^(-yrs))/i= 1087226.107597416
// $1 million

// Early Retirement, Long Lifespan
age_retirement = 55
age_death = 90
yrs = age_death - age_retirement = 35
pv = pmt*(1-(1+i)^(-yrs))/i= 1493169.058545419
// $1.5 million

// Average Retirement, Long Lifespan
age_retirement = 65
age_death = 90
yrs = age_death - age_retirement = 25
pv = pmt*(1-(1+i)^(-yrs))/i= 1249766.395492072
// $1.25 million

// Average Retirement, Average Lifespan
age_retirement = 65
age_death = 75
yrs = age_death - age_retirement = 10
pv = pmt*(1-(1+i)^(-yrs))/i= 648871.662348403
// $650,000

// Early Retirement, Short Lifespan
age_retirement = 55
age_death = 62
yrs = age_death - age_retirement = 7
pv = pmt*(1-(1+i)^(-yrs))/i= 480164.373595873
// $480,000