Question

1. What is the present value of the following 9-year annuities with discount rates of 5%?

a. The annuity grows at 3% per year with the first payment of $10,000 in one year.

c. The annuity grows at -5% per year with the first payment of $10,000 in three years

Answer 1

1-a	Present Value		$        79,465.79
working:
Annuties	Year	Cash flow	Discount factor	Present Value
1	1	$              10,000	0.9524	$         9,523.81
2	2	$              10,300	0.9070	$         9,342.40
3	3	$              10,609	0.8638	$         9,164.45
4	4	$              10,927	0.8227	$         8,989.89
5	5	$              11,255	0.7835	$         8,818.66
6	6	$              11,593	0.7462	$         8,650.68
7	7	$              11,941	0.7107	$         8,485.91
8	8	$              12,299	0.6768	$         8,324.27
9	9	$              12,668	0.6446	$         8,165.71
			Total	$      79,465.79
1-b	Present Value		$        53,853.57
Working:
Annuties	Year	Cash flow	Discount factor	Present Value
1	3	$              10,000	0.8638	$         8,638.38
2	4	$                 9,500	0.8227	$         7,815.67
3	5	$                 9,025	0.7835	$         7,071.32
4	6	$                 8,574	0.7462	$         6,397.86
5	7	$                 8,145	0.7107	$         5,788.54
6	8	$                 7,738	0.6768	$         5,237.25
7	9	$                 7,351	0.6446	$         4,738.47
8	10	$                 6,983	0.6139	$         4,287.19
9	11	$                 6,634	0.5847	$         3,878.88
			Total	$      53,853.57