Question

An investment pays $1,900 per year for the first 4 years, $3,800 per year for the next 7 years, and $5,700 per year the following 12 years (all payments are at the end of each year). If the discount rate is 7.70% compounding quarterly, what is the fair price of this investment?

Work with 4 decimal places and round your answer to two decimal places. For example, if your answer is $345.667 round as 345.67 and if your answer is .05718 or 5.718% round as 5.72.

Answer 1

Fair price of investment is   $ 39,539.86

Annual effecive interest rate	=	((1+(i/n))^n)-1	Where,
	=	((1+(0.0770/4))^4)-1	i	=	7.70%
	=	7.93%		n	=	4
Present Value of annuity of 1 for 4 years	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.0793)^-4)/0.0793	i	=	7.93%
	=	3.3173		n	=	4
Present Value of annuity of 1 for 7 years	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.0793)^-7)/0.0793	i	=	7.93%
	=	5.2189		n	=	7
Present Value of annuity of 1 for 12 years	=	(1-(1+i)^-n)/i	Where,
	=	(1-(1+0.0793)^-12)/0.0793	i	=	7.93%
	=	7.5634871		n	=	12
Present Value of 1 for 4 years	=	(1+i)^-n
	=	(1+0.0793)^-4
	=	0.73693858
Present Value of 1 for 11 years	=	(1+i)^-n
	=	(1+0.0793)^-11
	=	0.43195256
Present Value of $ 1900 per year for first 4 years	=	Annual cash flow	*	Present Value of annuity of 1 for 4 years
	=	$   1,900.00	*	3.3173
	=	$   6,302.86
Present Value of $ 3800 per year for next 7 years	=	Annual cash flow	*	Present Value of annuity of 1 for 7 years	*	Present Value of 1 for 4 years
	=	$   3,800.00	*	5.2189	*	0.73693858
	=	$ 14,614.71
Present Value of $ 5700 per year for next 12 years	=	Annual cash flow	*	Present Value of annuity of 1 for 12 years	*	Present Value of 1 for 11 years
	=	$   5,700.00	*	7.5635	*	0.43195256
	=	$ 18,622.29
Fair price of investment	=	Present Value of cash flow from investment
	=	$   6,302.86	+	$ 14,614.71	+	$ 18,622.29
	=	$ 39,539.86