Today is your 30th birthday and you must choose between two retirement

Today is your 30th birthday and you must choose between two retirement options. The first option will provide
you with 10 equal annual payments of $100,000 beginning on your 65th birthday.

The second option will
provide you with one payment of $1,000,000 on your 70th birthday. If the interest rate is 6 percent per year and
you are assured of living to at least 80 years of age, which option is better?

ANSWER

You must find the value of each option at the same point in time. The present value of the retirement annuity at age 65
is $780,169. The present value of the $1,000,000 at age 65 is $747,258. Therefore, the 10-year annuity is the better option.
Comparable values at age 70 are $1,044,042 for the annuity and $1,000,000 for the lump sum. At age 74, the value of the
annuity is $1,318,080 and the value of the lump sum is $1,262,477. Note that the ranking of the options does not change
regardless of the date used.