Question

6 Your mother is planning to retire this year. Her firm has offered her a lump sum retirement payment of S50,000 or a $6,000 lifetime annuity whichever she chooses. Your mother is in reasonably good health and expects to live for at least 15 more years. Which option should she choose, assuming that an 8% interest rate is her opportunity cost?

Answer 1

	Time value of money is a financial term which tells us that money in present term is worth more than that to be received in future.
	This because money which we have now can be invested and we can earn return on this investment which leads to larger sum of money in the future.
6)	In this question mother has two options either to receive lumpsum today of $50,000 or $6,000 per year for 15 years
	In both the options we will calculate to calculate the present worth and option which provides higher present worth would be better for mother as it would be worth higher in the future.
	Option 1
	Timeline
	PV					FV
	0	1	2	3	4	……….
	$50,000
	Today
	The present value of lumpsum $50,000 now is worth $50,000 today
	Option 2
	PV	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	$6,000	FV
	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	Value to be found
	Formula to calculate present value of $6,000 to be received each year for 15 years is
	Present Value of annuity = P[1-(1+r)^(-n)]/r
	Where P is the annuity to be received, $6,000
	r is the opportunity cost, 8%
	n is number of year annuity to be received, 15 years
	Present value of annuity = $6,000[1-(1+0.08)^(-15)]/0.08
			$6,000[1-0.31524]/0.08
			$6,000*(0.68476/0.08)
			$6,000*8.55950
			$51,357
	The present value of annuity is $51,357
	The annuity factors has been rounded to five decimal place
	The lifetime annuity has higher present value of $51,357 than the lumpsum payment of $50,000 and therefore she should choose lifetime annuity
7)	In this question we need to calculate the number of years steve will be able to withdraw if he withdraws $100,000 every year from $400,000 saved so far.
	Timeline
	PV	$100,000	$100,000	$100,000	$100,000	FV
	0	1	2	3	4	……….n
	$400,000					Number of years withdrawal value to be found - n
	Today
	Present Value of annuity = P[1-(1+r)^(-n)]/r
	$400,000 = $100,000*[1-(1+0.10)^(-n)]/0.10
	$400,000 = $100,000*[1-(1.10)^(-n)]/0.10
	400,000/100,000 = [1-(1.10)^(-n)]/0.10
	4 = [1-(1.10)^(-n)]/0.10
	So we get n = 5.36 years
	Steve can withdraw for 5.36 years $100,000 each year