Question

An insurance company is trying to sell you a retirement annuity. The annuity will give you 20 payments with the first payment in 12 years when you retire. The insurance firm is asking you to pay $50,000 today. If this is a fair deal, what must the payment amount be (to the dollar) if the interest rate is 8 percent?

please show in excel

Answer 1

Given

Rate of Interest = 8%

No.of Annuity payments = 20

Let the Annuity amount be X

We know that the Present value of the future Cash inflows is equal to the the present value of the todays cash outflow to determine fair Annuity installments

Year	S.No	Amount	Disc @ 8%	Discounting factor
12	1	X	1/(1.08)^12	0.3971
13	2	X	1/(1.08)^13	0.3677
14	3	X	1/(1.08)^14	0.3405
15	4	X	1/(1.08)^15	0.3152
16	5	X	1/(1.08)^16	0.2919
17	6	X	1/(1.08)^17	0.2703
18	7	X	1/(1.08)^18	0.2502
19	8	X	1/(1.08)^19	0.2317
20	9	X	1/(1.08)^20	0.2145
21	10	X	1/(1.08)^21	0.1987
22	11	X	1/(1.08)^22	0.1839
23	12	X	1/(1.08)^23	0.1703
24	13	X	1/(1.08)^24	0.1577
25	14	X	1/(1.08)^25	0.1460
26	15	X	1/(1.08)^26	0.1352
27	16	X	1/(1.08)^27	0.1252
28	17	X	1/(1.08)^28	0.1159
29	18	X	1/(1.08)^29	0.1073
30	19	X	1/(1.08)^30	0.0994
31	20	X	1/(1.08)^31	0.0920
		Total		4.2108

X * PVAF = $ 50,000

X * 4.2108 = $ 50,000

X = $ 50000/4.2108

X = $ 11874.228

Hence the Payment Amount should be $ 11874.228.

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