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. $500 per year for 16 years at 14%.

2. $250 per year for 8 years at 7%.

3. $1,000 per year for 16 years at 0%.

4. Rework previous parts assuming they are annuities due.

   Present value of $500 per year for 16 years at 14%:   

   Present value of $250 per year for 8 years at 7%:

   Present value of $1,000 per year for 16 years at 0%:

Answer 1

				Present value
a.	$500 per year for 16 years at 14%.			$          3,132.53
b.	$250 per year for 8 years at 7%.			$          1,492.82
c.	$1,000 per year for 16 years at 0%.			$       16,000.00
d.				Present value
	$500 per year for 16 years at 14%.			$          3,571.08
	$250 per year for 8 years at 7%.			$          1,597.32
	$1,000 per year for 16 years at 0%.			$       16,000.00
Working;
When payment is made at the end of period it is called as ordinary annuity and annuity due if made at the beginning of period.
Present value of ordinary annuity of 1	=	(1-(1+i)^-n)/i		Where,
(At the end of period)				i	=	Interest rate
				n	=	Time
Present value of annuity due of 1	=	((1-(1+i)^-n)/i)*(1+i)		Where,
(At the beginning of period)				i	=	Interest rate
				n	=	Time
Now,present value of both type of cash flow is calculated as follows:
	Payment	Years	Interest Rate	Present value	Present value
			(Annual)	(Payment made on last day of period)	(Payment made on first day of period)
				(Payment*Present value of ordinary annuity of 1)	(Payment*Present value of annuity due of 1)
a.	$                 500	16	14%	$          3,132.53	$             3,571.08
b.	$                 250	8	7%	$          1,492.82	$             1,597.32
c.	$             1,000	16	0%	$       16,000.00	$           16,000.00
a.	Present value of ordinary annuity of 1	=	(1-(1+0.14)^-16)/0.14	=	6.265059636
	Present value of annuity due of 1	=	((1-(1+0.14)^-16)/0.14)*(1+0.14)	=	7.142167985
b.	Present value of ordinary annuity of 1	=	(1-(1+0.07)^-8)/0.07	=	5.971298506
	Present value of annuity due of 1	=	((1-(1+0.07)^-8)/0.07)*(1+0.07)	=	6.389289402
Note:
	When interest rate is 0%, then present value is the sum of total cash flows.