Question

How much do you have to deposit today so that beginning 11 years from now you can withdraw ?$9,000 a year for the next 5 years? (periods 11 through 15?) plus an additional amount of $18,000 in the last year? (period 15?)? Assume an interest rate of 9 percent.

Answer 1

Amount to be deposited should be equal to present value of cash flow.
a.
	Present Value of annual cash flow				=	Annual cash flow x cumulative discount factor
	(At stand point of 11 years from now)				=	$          9,000	x	4.23972
					=	$        38,157
	Working:
	Cumulative discount factor				=	((1-(1+i)^-n)/i)*(1+i)			Where,
					=	((1-(1+0.09)^-5)/0.09)*(1+0.09)			i	9%
					=	4.23972			n	5
b.	Present Value of above amount				=	$        38,157	x 1.09^-11
					=	$        14,787
c.	Present value of last period cash flow				=	$        18,000	x 1.09^-15
					=	$          4,942
d.	Present value of b. and c.				=	$        14,787	+	$    4,942
					=	$        19,729
So, required amount to be deposited today is					$ 19,729