Question

If you can earn 10% on your savings account, which of the following investments is worth more to you?
(1) $5,000 in 3 years;
(2) A 5-year ordinary annuity offering $900 payments
Please explain

Answer 1

1) $ 5000 in 3 Years

Computation of the Present value

Year	Cash flow	Disc @ 10%	Discounted Cash flows
0	$0.00	1	$0.00
1	$0.00	0.909091	$0.00
2	$0.00	0.826446	$0.00
3	$5,000.00	0.751315	$3,756.57

So the Present Value of $ 5000 received after 3 years is $ 3756.57

2)5 Year Annuity offering $ 900 payments( Assuming annuity received at the end of the year)

Computation of the Present value

Year	Cash flow	Disc @ 10%	Discounted Cash flows
1	$900	0.909091	$818.18
2	$900	0.826446	$743.80
3	$900	0.751315	$676.18
4	$900	0.683013	$614.71
5	$900	0.620921	$558.83
	Total		$3,411.71

The Present value of the Annuity received at the end of the year is $ 3411.71

Assuming annuity is received at the begining of the year then present value is

Year	Cash flow	Disc @ 10%	Discounted Cash flows
1	$900	1	$900.00
2	$900	0.909091	$818.18
3	$900	0.826446	$743.80
4	$900	0.751315	$676.18
5	$900	0.683013	$614.71
	Total		$3,752.88

Present value of annuity received at begining of the year is $ 3752.88

Decision making: The present value of $ 5000 to be received after 3 years is greather than Annuity.So it is better to receive $ 5000 after 3 years than Annuity