you plan to retire 35 years from today. You want to invest the same amount each year starting one year from now so you can withdraw $50000 each year during your retirement. You expect to live independently for 25 years following your retirement. You also need a lump sum of 350000 in 60 years to pay for permanent nursing care until you die. You earn 10% per year. You intend to make your first withdrawal one year after retiring. How much do you need to invest each year?
Needed FV (lumpsum in 60 years) = $ 350,000
So , PV of the lumpsum in 35 years time as on retirement date = PV ( 350,000 @ 10% for 25 years) = 350,000/(1+10%)^25 = $ 32,303.60
Withdrawals in retirement (PMT) = 50,000
Years of retirement (nper) = 25 years
rate = 10%
PV of withdrawals 35 years from now (PV) = = $ 453,852
So Total PV 35 years from now (FV) =( PV of withdrawals 35 years from now (PV) + PV of the lumpsum in 35 years time as on retirement date) = $ 486,155.60
Rate = 10%
Number of years (nper) = 35 years
Investment per year for 35 years time (PMT) = = $ 1,793.77
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