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 Treasur

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 539 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:

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.

PVA_{month 539} = $__________= $_________(__________)= $______________

Premium and price to Insurance Company

Price = $___________ (1.050) = $____________

Value of Current Savings in 539 months (assuming monthly compounding.

FV_{539 months} = $60,000 (1._______)⁵³⁹= $60,000 (____________)= $___________

Total New Saving needed by month 539 =$_____________

Saving Each month for next 539 Months.

= $_______________

Then,

A = $____________ /______________ = $__________ per month