3. Assume todays U.S. Treasury Yield Curve is given below. You can use this to estimate the average rate of inflation for the next thirty years as the difference between the nominal rate on a 30-Year Treasury bond and the Inflation Indexed Treasury bond- (often called Treasury Inflation Protected bonds or TIPs-Real Rate). The shape of the Yield Curve also tells us something about future interest rates.

http://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/Historic-Yield-Data-Visualization.aspx

Nominal Rates: ₀R₁ = 1.31% ₀R₂ = 1.45% ₀R₃ = 1.59% ₀R₄ = 1.74% ₀R₅ = 1.89% ₀R₆ = 2.03% ₀R₇ = 2.13% ₀R₁₀ = 2.31% ₀R₂₀ = 2.63% ₀R₃₀ = 2.87%

Real Rates: ₀r₅ = 0.16% ₀r₇ = 0.37% ₀r₁₀ = 0.44% ₀r₂₀ = 0.74% ₀r₃₀ = 0.92%

Your 27 year old client wants to retire when he is 70 years old with a retirement income equivalent to $8,000 per month in todays dollars. To estimate the market expectations for average annual inflation for the next 43 years, use the difference between the nominal rate and real rate (rate on TIPs) for the 30-year Treasury rates given above. Because of inflation, your client will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a guaranteed lifetime annuity from an insurance company one month before he retires (515 months from now). The retirement annuity will begin in exactly 43 years (516 months). At the time the retirement annuity is purchased, the insurance company will add a 5.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is the actuarial cost to the insurance company of his anticipated lifetime annuity. He has savings of $80,000 today that will be invested at an annual return of 6.00%. Given a rate of return of 6.00% for the foreseeable future, how much does he need to save each month (total of 515 payments) until the month before he retires? He will make the first payment next month and the last payment one month before he retires. For life expectancy after retirement, use the Cohort Life Tables for Social Security Area by Sex table below:

Cohort Life Tables for Social Security by Sex
Male				Female
	Probability	# of 100,000	Life		Probability	# of 100,000	Life
Age	Death	Living	Expectancy	Age	Death	Living	Expectancy
40	0.00170	96,759	42.94	40	0.00108	98,088	46.22
41	0.00183	96,595	42.01	41	0.00116	97,982	45.27
42	0.00196	96,418	41.09	42	0.00123	97,869	44.33
43	0.00209	96,229	40.17	43	0.00129	97,749	43.38
44	0.00223	96,028	39.25	44	0.00135	97,622	42.43
45	0.00238	95,814	38.33	45	0.00142	97,490	41.49
46	0.00254	95,586	37.43	46	0.00150	97,352	40.55
47	0.00268	95,343	36.52	47	0.00159	97,205	39.61
48	0.00278	95,088	35.62	48	0.00168	97,051	38.67
49	0.00288	94,823	34.71	49	0.00178	96,888	37.74
50	0.00299	94,550	33.81	50	0.00190	96,715	36.80
51	0.00313	94,268	32.91	51	0.00204	96,532	35.87
52	0.00331	93,973	32.01	52	0.00221	96,335	34.94
53	0.00355	93,662	31.12	53	0.00241	96,123	34.02
54	0.00385	93,329	30.23	54	0.00265	95,891	33.10
55	0.00419	92,970	29.34	55	0.00292	95,637	32.19
56	0.00457	92,581	28.46	56	0.00322	95,358	31.28
57	0.00497	92,158	27.59	57	0.00354	95,051	30.38
58	0.00539	91,700	26.73	58	0.00386	94,714	29.49
59	0.00585	91,205	25.87	59	0.00420	94,348	28.60
60	0.00635	90,672	25.02	60	0.00457	93,952	27.72
61	0.00693	90,096	24.18	61	0.00500	93,522	26.84
62	0.00763	89,472	23.34	62	0.00551	93,054	25.97
63	0.00847	88,790	22.52	63	0.00613	92,541	25.12
64	0.00944	88,038	21.70	64	0.00683	91,974	24.27
65	0.01053	87,206	20.91	65	0.00762	91,346	23.43
66	0.01167	86,288	20.12	66	0.00845	90,650	22.61
67	0.01284	85,281	19.36	67	0.00930	89,884	21.80
68	0.01402	84,186	18.60	68	0.01014	89,048	21.00
69	0.01523	83,006	17.86	69	0.01101	88,145	20.21
70	0.01660	81,742	17.13	70	0.01199	87,175	19.42
71	0.01811	80,385	16.41	71	0.01308	86,130	18.65
72	0.01965	78,929	15.70	72	0.01419	85,003	17.89
73	0.02119	77,378	15.01	73	0.01533	83,797	17.15
74	0.02280	75,739	14.32	74	0.01653	82,513	16.40
75	0.02479	74,012	13.64	75	0.01804	81,148	15.67
76	0.02713	72,177	12.98	76	0.01979	79,685	14.95
77	0.02954	70,219	12.32	77	0.02154	78,107	14.24
78	0.03200	68,144	11.68	78	0.02321	76,425	13.54
79	0.03469	65,964	11.05	79	0.02502	74,651	12.85

Expected Inflation =

Expected Remaining Life in Months at Retirement =

Needed per month retirement income.

FV_{43 years} = $8,000 (1._______)⁴³ = $8,000 (________) = $___________

Total amount Needed in retirement account one month (month 515) before retirement.

PVA_{month 515} = $_________[(1-(1+0.___)^-____)/0.____]= $________(_________)= $_________

Premium and price to Insurance Company

Price = $__________ (1.050) = $____________

Value of Current Savings in 515 months (assuming monthly compounding.

FV_{515 months} = $80,000 (1._____)⁵¹⁵ = $80,000 (_________)= $__________

Total New Saving needed by month 515 = $___________

Saving Each month for next 515 Months.

fva= a[(((1+r)^n)-1)/r]= $___________[(((1+0.___)^515)-1)/0.____ ]

Then,

A = $___________ /_______________ = $____________ per month