Question

6. Calculating Annuity Values. For each of the following annuities, calculate the present value.

Annuity Payment Years Interest Rate

  $2,100    7 5%

1,095    9 10%

   11,000 18 8%   

30,000 28 14%

Answer 1

a.	Present value of annuities		=	Annuity	*	Present value of annuity of 1
			=	$             2,100	*	5.786373
			=	$     12,151.38
	Working:
	Present value of annuity of 1		=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.05)^-7)/0.05			i	0.05
			=	5.786373397			n	7
b.	Present value of annuities		=	Annuity	*	Present value of annuity of 1
			=	$             1,095	*	5.759024
			=	$       6,306.13
	Working:
	Present value of annuity of 1		=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.10)^-9)/0.10			i	0.10
			=	5.759023816			n	9
c.	Present value of annuities		=	Annuity	*	Present value of annuity of 1
			=	$           11,000	*	9.371887
			=	$ 1,03,090.76
	Working:
	Present value of annuity of 1		=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.08)^-18)/0.08			i	0.08
			=	9.371887136			n	18
d.	Present value of annuities		=	Annuity	*	Present value of annuity of 1
			=	$           30,000	*	6.960662
			=	$ 2,08,819.87
	Working:
	Present value of annuity of 1		=	(1-(1+i)^-n)/i			Where,
			=	(1-(1+0.14)^-28)/0.14			i	0.14
			=	6.96066228			n	28