Question

A man is planning to retire in 15 years. Money can be deposited at 8% interest compounded quarterly, and it is also estimated that the future general inflation rate will be 6%. What amount of end-of-quarter deposit must be made each quarter until the man retires so that he can make annual withdrawals of $80,000 in terms of today's dollars over the 20 years following his retirement? (Assume that his first withdrawal occurs at the end of the first year after his retirement.) (Without using excel)

Answer 1

	If you invest PV at I% for Y years compounded quarterly then the FV is:
	FV=PV*(1+I/4)^(Y*12)
	If inflation is running at F% per annum the FV will only be worth:
	FV*(1-F)^Y
	Putting these two together gives the estimate of FV in today's terms as:
	FV=PV*(1+I/4)^(Y*4)*(1-F)^Y
	PV	Amount to be deposited
	I	Interest Rate	8%
	F	Inflation		6%
	Y	No of year	15 year
	Annuit factor from 16-35 years @8%	3.092
	Discount factor @8% in 15 year	0.315
	Future value at the start of year 16(FV)	232518.4	(80000*1-6%)*3.092
	Future value at the start of year 0(FV)	73243.3	(232518.4*0.315)
	(By applying in formula)
	232518=PV*(1+8%/4)^(15*4)*(1-6%)^15
	PV	73243			73243	$56,515
		(1+8%/4)^(15*4)*(1-6%)^15	1.296
	Amount to be deposited=$56,515