Question

Suppose you wish to retire forty years from today. You determine that you need RM 50,000 per year once you retire, with the first retirement funds withdrawn one year from the day you retire. You estimate that you will earn 6% per year on your retirement funds and that you will need funds up to and including your 25th birthday after retirement

a) How much must you deposit in an account today so that you have enough funds for retirement?

b)How much must you deposit each year in an account, starting one year from today, so that you have enough funds for retirement

Answer 1

	Let's first calculate the PV of the retirement corpus
	PV of annuity
	P = PMT x (((1-(1 + r) ^- n)) / r)
	Where:
	P = the present value of an annuity stream	P
	PMT = the dollar amount of each annuity payment	$       50,000
	r = the effective interest rate (also known as the discount rate)	6%
	n = the number of periods in which payments will be made	25
	PV of retirement corpus required=	50000*(((1-(1+6%) ^-25)) /6%)
	PV of retirement corpus required=	$639,167.81
Solution a	Lump-sum deposit required today=	639167.81/(1+6%)^40
	Lump-sum deposit required today=	$ 62,141.29
Solution b	Annual deposits
	FV of annuity
	P = PMT x ((((1 + r) ^ n) - 1) / r)
	Where:
	P = the future value of an annuity stream	$639,167.81
	PMT = the dollar amount of each annuity payment	PMT
	r = the effective interest rate (also known as the discount rate)	6%
	n = the number of periods in which payments will be made	40
	FV of annuity=	PMT x ((((1 + r) ^ n) - 1) / r)
	639167.81=	PMT*((((1+6%)^40)-1)/6%)
	Annual deposit=	639167.81/((((1+6%)^40)-1)/6%)
	Annual deposit=	$    4,130.01