Question

1. Jack Straw is now 65 years old and has accumulated $850,000 for his retirement. He wants this sum to pay a steady annual income for the next twenty years, starting one year from now. Assuming a discount rate of 3.45% p.a., what kind of annual income can he expect for the twenty year period?         

2. You won a “$50,000” prize which will be paid in annual installments under one of two options as follows: (figures in thousands of dollars)

Year	1	2	3	4	5
Option A	5	5	10	10	20
Option B		10	15	20	5

Using a discount rate of 5.7%, which option would you choose and why?

Answer 1

1)	$850,000 is the present value of the amount receivable at the
	end of each year for 20 years when discounted at 3.45%.
	The amount receivable is an annuity.
	Hence, 850000 = A*(1.0345^20-1)/(0.0345*1.0345^20)
	where A = the annuity amount.
	Solving for A = 850000*0.0345*1.0345^20/(1.0345^20-1) =	$ 59,536.66
2)	PV of Option A = 5000/1.057+5000/1.057^2+10000/1.057^3+10000/1.057^4+20000/1.057^5 =	$ 40,843.24
	PV of Option B = 10000/1.057^2+15000/1.057^3+20000/1.057^4+5000/1.057^5 =	$ 41,464.49
	As Option B has higher PV it should be chosen.