Question

1. You just retired with $1m! You are now planning your retirement distributions over the next 30 years. You expect to earn 6% annually and you expect inflation to be 3% annually. To ensure your purchasing power is maintained, you've decided you'd like to withdraw the same amount each year in terms purchasing power. Please provide me with the following information: 1) the real rate of interest (do not approximate), 2) the real and nominal amount of your withdrawals in years 1, 10, an of d 30. (8 Points)

Answer 1

	Nominal Rate of return	6%
	Inflation	3%
	Real rate=	((1+6%)/(1+3%)-1)
	Real rate=	2.9126%
	To support inflation backing, annuity should be increased each year by 3%
	PV of annuity for growing annuity
	P = (PMT/(r-g)) x (1-((1+g)/(1 + r)) ^n)
	Where:
	P = the present value of an annuity stream
	PMT = the dollar amount of each annuity payment
	r = the effective interest rate (also known as the discount rate)
	i=nominal Interest rate
	n = the number of periods in which payments will be made
	g= Growth rate
	PV	1000000
	R=	6%
	Years	30
	Growth rate	3%
	1000000=	(PMT/(6%-3%)) x (1-((1+3%)/(1 + 6%)) ^30)
	1000000=	(PMT/(6%-3%)) * 0.577389
	(PMT/(6%-3%))=	1000000/0.5777389
	(PMT/(6%-3%))=	1,731,934.58
	PMT=	51,958.04
	So First annual payment by 51,958.04 which should increase by 3% every year
		Nominal withdrawal	Nominal withdrawal
	T1	51,958.04	51,958.04
	T10	51958.04*(1+3%)^9	67,793.46
	T30	51958.04*(1+3%)^29	122,442.52
		Real withdrawal	Real withdrawal
	T1	51958.04/(1+3%)^1	50,444.70
	T10	67793.46/(1+3%)^10	50,444.70
	T30	122442.52/(1+3%)^30	50,444.70