Question

Suppose you are going to receive $11,000 per year for 7 years. The appropriate interest rate is 7 percent.

  

a. What is the present value of the payments if they are in the form of an ordinary annuity?

b. What is the present value if the payments are an annuity due?

c. Suppose you plan to invest the payments for 7 years, what is the future value if the payments are an ordinary annuity?

d. Suppose you plan to invest the payments for 7 years, what is the future value if the payments are an annuity due?

Answer 1

a.	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$     11,000.00	*	5.389289
		=	$     59,282.18
	Working:
	Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
		=	(1-(1+0.07)^-7)/0.07		i	7%
		=	5.389289402		n	7
b.	Present value	=	Annual cash flow	*	Present value of annuity of 1
		=	$     11,000.00	*	5.76654
		=	$     63,431.94
	Working:
	Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
		=	((1-(1+0.07)^-7)/0.07)*(1+0.07)		i	7%
		=	5.76653966		n	7
c.	Future value	=	Annual cash flow	*	Future value of annuity of 1
		=	$     11,000.00	*	8.654021
		=	$     95,194.23
	Working:
	Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
		=	(((1+0.07)^7)-1)/0.07		i	7%
		=	8.654021093		n	7
d.	Future value	=	Annual cash flow	*	Future value of annuity of 1
		=	$     11,000.00	*	9.259803
		=	$ 1,01,857.83
	Working:
	Future value of annuity of 1	=	((((1+i)^n)-1)/i)*(1+i)		Where,
		=	((((1+0.07)^7)-1)/0.07)*(1+0.07)		i	7%
		=	9.259802569		n	7