Question

Can you explain this?

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(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 See http://www.ambest com/home/default.aspx AM Best is the only global credit rating agency with a unique focus on the insurance industry-

Expected Inflation = Expected Remaining Life in Months at Retirement = Needed per month retirement income. FV 45 Years = \$8,000 (1 45 = \$8,000( ) = \$ Total amount Needed in retirement account one month (month 539) before retirement. PXAugust 539 = \$ 1 -( + \$ Premium and price to Insurance Company Price = \$ (1.050) = \$ Value of Current Savings in 539 months (assuming monthly compounding. FV:39 months = \$60,000 (1. )\$39 = \$60,000 ( = S Total New Saving needed by month 539 = Saving Each month for next 539 Months. FVA _ _ (+ ) - 1 = \$ A. Then, A = \$ per month