Question

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent.

1. $200 per year for 14 years at 4%.

   $  

2. $100 per year for 7 years at 2%.

   $  

3. $200 per year for 8 years at 0%.

   $  

4. Rework previous parts assuming they are annuities due.

   Present value of $200 per year for 14 years at 4%: $  

   Present value of $100 per year for 7 years at 2%: $  

   Present value of $200 per year for 8 years at 0%: $  

Answer 1

1)
a.	Present value of ordinary annuities	$        2,112.62
Working:
# 1	Present value of annuity of 1	=	(1-(1+i)^-n)/i	Where,
		=	(1-(1+0.04)^-14)/0.04	i	Interest rate	4%
		=	10.56312293	n	Number of period	14
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       200.00	*	10.563123
		=	$                                   2,112.62
b.	Present value of ordinary annuities	$            647.20
	Working:			Where,
# 1	Present value of annuity of 1	=	(1-(1+0.02)^-7)/0.02	i	Interest rate	2%
		=	6.471991069	n	Number of period	7
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       100.00	*	6.4719911
		=	$                                       647.20
c.	Present value of ordinary annuities	$            800.00
	Working:			Where,
# 1	Present value of annuity of 1	=	1*8	i	Interest rate	0%
		=	8	n	Number of period	8
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       100.00	*	8
		=	$                                       800.00
2)
a.	Present value of annuities due	$        2,197.13
	Working:
# 1	Present value of annuity of 1	=	((1-(1+i)^-n)/i)*(1+i)	Where,
		=	((1-(1+0.04)^-14)/0.04)*(1+0.04)	i	Interest rate	4%
		=	10.98565	n	Number of period	14
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       200.00	*	10.98565
		=	$                                   2,197.13
b.	Present value of annuities due	$            660.14
	Working:			Where,
# 1	Present value of annuity of 1	=	((1-(1+0.02)^-7)/0.02)*(1+0.02)	i	Interest rate	2%
		=	6.601430891	n	Number of period	7
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       100.00	*	6.6014309
		=	$                                       660.14
c.	Present value of annuities due	$            800.00
	Working:			Where,
# 1	Present value of annuity of 1	=	1*8	i	Interest rate	0%
		=	8	n	Number of period	8
# 2	Present value of annuities	=	Annuities*Present value of annuity of 1
		=	$                                       100.00	*	8
		=	$                                       800.00
Note:
	In case of ordinary annuities, payments are made at the end of period.
	In case of annuities due, payments are made at the beginning of period.