(45 pta) 3. Assume today's 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.

U.S. Treasury Yield Curve (Nominal Rates)

Date

2 00

309 609 185 2 86 386 5 85 7 85 10 4 20 4 30 45

08/19/19

2.01

1.99

1.93

1.92 1.88 1.74 1.68 1.66 1.73 1.79 2.04 2.22

U.S Treasury Yield Curve (Real Rates-TIPS)

DATE

5 YR

7 YR

10 YR

20 YR

30 YR

08/19/19

0.25

0.21

0.18

0.38

0.57

Your 25 year old client wants to retire when he is 70 years old, and have a retirement income

equivalent to $8,000 per month in today's (inflation adjusted) dollars. To estimate the market

expectations for average annual inflation for the next 45 years, use the difference between the nominal

rate and real rate on TIPs for the 30-year Treasury rates given above. Because of inflation, he will

need substantially higher retirement monthly income to maintain the same purchasing power. He plans

to purchase a guaranteed lifetime annuity from a AAA rated insurance company' one month before he

retires (539 months from now). The retirement annuity will begin in exactly 45 years (540 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 of his anticipated lifetime annuity. He has savings of $60,000 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 $39 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

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