Question

# you plan to retire 35 years from today. You want to invest the same amount each...

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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