Question

Computing the Value of Deferred Annuity

What is the present value of 6 years of annual cash receipts of $40,800 at the end of each year that begins two years from today, assuming a 4% interest rate?

Please show work and formula(s)!

Answer 1

This is a case of an ordinary annuity.

Ordinary Annuity - It is Equalised annual investments made at the end of each period

Let us caluculate the present value of annuity two years from today.

Formula for present value of annuity is

For Ordinary Annuity - P*((1-(1+r)^-n)/r

P = Equalised annual payment

n = number of periods

r = rate on interest

Present value = 40800 * 5.242136 = 213879.18

This present value is 2 years from now

Hence we will discount it twice with factor 1.04

= 213879.18/(1.04*1.04) = $197743.16

Hence the required present value is $197743.16

For better understanding use the below table.

Year	Annual Cash Flow	Disount factor	Present Value 2 years from now
3.00	40,800.00	0.96	39,230.77
4.00	40,800.00	0.92	37,721.89
5.00	40,800.00	0.89	36,271.05
6.00	40,800.00	0.85	34,876.01
7.00	40,800.00	0.82	33,534.63
8.00	40,800.00	0.79	32,244.83