Question

For each of the following annuities, calculate the annual cash flow. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)

Cash Flow				Present Value			Years				Interest Rate
		$		$	32,000			6					7	%
					29,050			8					5
					153,500			16					10
					223,500			21					9

Answer 1

Cash flow		Present Value		Years	Interest rate
$    6,713.47		$       32,000		6	7%
$    4,494.67		$       29,050		8	5
$   19,619.85		$     1,53,500		16	10
$   24,052.32		$     2,23,500		21	9
Working:
i.
Present Value of Annuities			=	Annual Cash flow x Cumulative discount factor
or,	Annual Cash flows		=	Present Value of Annuities/Cumulative discount factor
ii.
At 7%
Cumulative discount factor			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.07)^-6)/0.07		i	Interest Rate		7%
			=	4.7665		n	Years		6
At 5%
Cumulative discount factor			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.05)^-8)/0.05		i	Interest Rate		5%
			=	6.4632		n	Years		8
At 10%
Cumulative discount factor			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.10)^-16)/0.10		i	Interest Rate		10%
			=	7.8237		n	Years		16
At 9%
Cumulative discount factor			=	(1-(1+i)^-n)/i		Where,
			=	(1-(1+0.09)^-21)/0.09		i	Interest Rate		9%
			=	9.2922		n	Years		21
iii.
Interest Rate		Present Value of annuities			Cumulative discount factor			Annual Cash flows
		a			b			a/b
7%		$       32,000			4.7665			$ 6,713.47
5		$       29,050			6.4632			$ 4,494.67
10		$     1,53,500			7.8237			$19,619.85
9		$     2,23,500			9.2922			$24,052.32