Question

Suppose you are going to receive $9,000 per year for 6 years. The appropriate interest rate is 9 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 6 years, what is the future value if the payments are an ordinary annuity?

d. Suppose you plan to invest the payments for 6 years, what is the future value if the payments are an annuity due?

Answer 1

a.	Present value			$ 40,373.27
Working:
Present value of ordinary annuity of 1			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.09)^-6)/0.09		i	9%
			=	4.48591859		n	6
Present value of annuity			=	Annuity	x	Present value of annuity of 1
			=	$         9,000	x	4.485919
			=	$ 40,373.27
b.	Present value			$ 44,006.86
Working:
Present value of annuity due of 1			=	((1-(1+i)^-n)/i)*(1+i)		Where,
			=	((1-(1+0.09)^-6)/0.09)*(1+0.09)		i	9%
			=	4.88965126		n	6
Present value of annuity			=	Annuity	x	Present value of annuity of 1
			=	$         9,000	x	4.889651
			=	$ 44,006.86
c.	Future value			$ 67,710.01
Working:
Future value of ordinary annuity of 1			=	(((1+i)^n)-1)/i		Where,
			=	(((1+0.09)^6)-1)/0.09		i	9%
			=	7.52333456		n	6
Future value of annuity			=	Annuity	x	Future value of annuity of 1
			=	$         9,000	x	7.523335
			=	$ 67,710.01
d.	Future value			$ 73,803.91
Working:
Future value of annuity due of 1			=	((((1+i)^n)-1)/i)*(1+i)		Where,
			=	((((1+0.09)^6)-1)/0.09)*(1+0.09)		i	9%
			=	8.20043468		n	6
Future value of annuity			=	Annuity	x	Future value of annuity of 1
			=	$         9,000	x	8.200435
			=	$ 73,803.91