This comment is about the Straight Dope article, If I win the lottery, should I ask for a lump sum or an annuity?, dated March 2, 2004, located at the following link:
http://www.straightdope.com/columns/read/2149/if-i-win-the-lottery-should-i-ask-for-a-lump-sum-or-an-annuity
The article makes the following statement about the equivalence:
The cash value or present value of an annuity is the amount of money, today, that is mathematically equivalent to the sum of the payments, given a particular interest rate. By equivalent I mean that, if you deposited the cash value in an account bearing the agreed-upon interest rate for the term of the annuity, the accumulated amount would equal the face value.
The cash value is mathematically equivalent to the series of payments—not the sum, or face value. For example you would only need 3.72% annual interest rate to grow $500K to $1M in 19 years, which conflicts with the stated California Lottery example of $1M face value, $500K present value, $50K period payment, at 8.92% rate. I agree with the 8.92% annuity vs present value analysis; it’s the quoted text that I think should be corrected.