Question

Please show calculations/formulas.

Suppose you are going to receive $12,800 per year for five years. The appropriate interest rate is 7.7 percent.

  

a-1.	What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

a-2.	What is the present value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b-1.	Suppose you plan to invest the payments for five years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b-2.	Suppose you plan to invest the payments for five years. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Answer 1

a-1.	Present value	=	Annual cash flow	x	Present value of annuity of 1
		=	$       12,800	x	4.02448
Working:		=	$ 51,513.35
Present value of annuity of 1	=	(1-(1+i)^-n)/i		Where,
	=	(1-(1+0.077)^-5)/0.077		i	7.70%
	=	4.02448		n	5
a-2.	Present value	=	Annual cash flow	x	Present value of annuity of 1
		=	$       12,800	x	4.334365
Working:		=	$ 55,479.87
Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
	=	((1-(1+0.077)^-5)/0.077)*(1+0.077)		i	7.70%
	=	4.334365		n	5
b-1.	Future value	=	Annual cash flow	x	Future value of annuity of 1
		=	$       12,800	x	5.831608
Working:		=	$ 74,644.58
Future value of annuity of 1	=	(((1+i)^n)-1)/i		Where,
	=	(((1+0.077)^5)-1)/0.077		i	7.70%
	=	5.831608		n	5
b-2.	Future value	=	Annual cash flow	x	Future value of annuity of 1
		=	$       12,800	x	6.280642
Working:		=	$ 80,392.21
Future value of annuity of 1	=	((((1+i)^n)-1)/i)*(1+i)		Where,
	=	((((1+0.077)^5)-1)/0.077)*(1+0.077)		i	7.70%
	=	6.280642		n	5