Question

7. An annuity provides for 30 annual payments. The first payment of 100 is made immediately and the remaining payments increase by 8% per year. Interest is calculated at an annual effective interest rate of 13.4% per year. Calculate the present value of the annuity. Give your answer rounded to the nearest whole number. Answer:

Answer 1

Solution:

Computation of Present value of annuity
Period	Annuity	PV factor (13.4%)	Present value
1	$100.00	0.88183	$88.18
2	$108.00	0.77763	$83.98
3	$116.64	0.68574	$79.98
4	$125.97	0.60471	$76.18
5	$136.05	0.53325	$72.55
6	$146.93	0.47024	$69.09
7	$158.69	0.41468	$65.80
8	$171.38	0.36568	$62.67
9	$185.09	0.32246	$59.69
10	$199.90	0.28436	$56.84
11	$215.89	0.25076	$54.14
12	$233.16	0.22113	$51.56
13	$251.82	0.19500	$49.10
14	$271.96	0.17196	$46.77
15	$293.72	0.15164	$44.54
16	$317.22	0.13372	$42.42
17	$342.59	0.11792	$40.40
18	$370.00	0.10398	$38.47
19	$399.60	0.09170	$36.64
20	$431.57	0.08086	$34.90
21	$466.10	0.07131	$33.24
22	$503.38	0.06288	$31.65
23	$543.65	0.05545	$30.15
24	$587.15	0.04890	$28.71
25	$634.12	0.04312	$27.34
26	$684.85	0.03802	$26.04
27	$739.64	0.03353	$24.80
28	$798.81	0.02957	$23.62
29	$862.71	0.02607	$22.50
30	$931.73	0.02299	$21.42
Total			$1,423