Question

You plan to retire 35 years from now. You expect that you will live 25 years after retiring. You want to have enough money upon reaching retirement age to withdraw $180,000 from the account at the beginning of each year you expect to live, and yet still have $2,500,000 left in the account at the time of your expected death (60 years from now). You plan to accumulate the retirement fund by making equal annual deposits at the end of each year for the next 35 years. You expect that you will be able to earn 12% per year on your deposits. However, you only expect to earn 6% per year on your investment after you retire since you will choose to place the money in less risky investments. What equal annual deposits must you make each year to reach your retirement goal?

Answer 1

Present value of retirement benefits at the age of retirement
Present value of annuity of 180000 at the time of retirement	Using present value function in MS excel	Pv(rate,nper,pmt,fv,type) rate = 6% nper = 25 pmt =180000 fv = 0 type =1	PV(6%,25,180000,0,1)	($2,439,064.35)
present value of 2500000 left in account at the time of retirement	Using present value function in MS excel	Pv(rate,nper,pmt,fv,type) rate = 6% nper = 25 pmt =0 fv = 2500000 type =0	PV(6%,25,0,2500000,1)	($582,496.58)
total funds would be accumulated at the time of retirement				($3,021,560.93)
Yearly amount to be saved to get the funds accumulated	Using PMT function in MS excel	pmt(rate,nper,pv,fv,type) rate = 12% nper =35 pv = 0 fv= 3021560.93 type =0	PMT(12%,35,0,3021560.93,0)	($6,999.81)
You should save 6999.81 or 7000 Approx per year to accumulate a fund