Question

How much must you deposit each year into your retirement account starting now and continuing through year 14 if you want to be able to withdraw $90,000 per year forever, beginning 28 years from now? Assume the account earns interest at 15% per year. The amount to be deposited is determined to be $ ____?

Answer 1

First present value in 28 years from now of perpetual withdrawal of $90,000 shall be calculated Present value of perpetual cash flows Perpetual annuity amount/ Interest rate Perpetual annuity amount Interest rate Present value of perpetual cash flows in year-28 $90,000 15% $600,000 [$90,000 / 15%) Second, present value of $600,000 in year-14 shall be calculated: Present value of perpetual cash flows in year-28 Discount factor @ 15% for 14 years Present value of $600,000 in year-14 $600,000 0.14133 $84,797.19 [1/(1+15%)14 as there are 14 years between year-14 and 28] [$600,000 x 0.14133] Finally, considering $84,797.19 as the target maturity value in year-14 from today, annual deposits starting today shall be calculated Annual Interest rate, RATE # of years of deposits, NPER Initial deposit in account, PV Balance in account at the end, FV Annual deposit type, TYPE Annual deposits required 15% 14 $0 $84,797.19 [As calculated in second step] :0 if deposited at the end of each year; 1 if deposited at the beginning of each year $1,820.45 [Ref: NOTE]

NOTE Annual deposits required is calculated using EXCEL FUNCTION PMT(rate,nper, pv,fv,type) where rate-15%; nper-14, pv:0; fv-84797.19; type-1; Here, value for pmt is input as negative figure because it denotes cash inflow; type-1 as annual deposits made at the beginning of each year. 15% 14 $o 1 Annual Interest rate, RATE 2 # of years of deposits, NPER 3 Initial deposit in account, PV 4 Balance in account at the end, FV 5 Annual deposit type, TYPE 6 Annual deposits required $84,797.19 [As calculated in second step] -PMT(B1,B2,B3,-B4,B5) [Ref: NOTE]