A pension fund has accumulated $1 million in a retirement plan for James B. Smit

Question

A pension fund has accumulated $1 million in a retirement plan for James B.
Smith, who retired this month at age 65. If Mr. Smith has a life expectancy of 75
years, what is the minimum size of the annual annuity check the pension plan
will be able to send him each year (assuming that the value of the pension fund’s
investments remains stable)? Should he insist on receiving that size payment
each year? Why or why not? What other kinds of information would be helpful
in analyzing Mr. Smith’s financial situation at retirement?

Explanation / Answer

we have PV of Annuity = $1M for n=10 Yrs (75-65), We need to find Annual payments PMT so that FV = 0 at end of 10 yrs or age 75 yrs ie PMT=PMT(Rate,nper,PV,FV) = PMT(,10,-1000000,0) = $100,000 This is assuming 0% returns. However The average rate of inflation is about 3% per year. Also the cost of health care has gone up 5.5% during the same period. So avge Rate on return should be 5.5%+3%=8.3% If 8.3% rate is assumed, then annual payment is PMT = PMT(8.3%,10,-1000000,0) = $151,052.29 It will hekp if rate of rerun on Pension plan is given along with inflation rate & cost of health insurnce

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