Lottery Winner’s Dilemma: Lump Sum or Annuity? Calculating the Present Value of an Annuity.

Posted June 9th, 2016.

Categories: The Calculating Lawyer.

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What if you won the lottery tomorrow, and your jackpot was $60,000 a year for 15 years? That would come to $900,000!  But, of course, you would have to wait 15 years to collect it all. What if you could take a smaller amount today in a single lump sum payment?

What amount today would be worth trading away $60,000 for 15 years?

The question can be answered by using the formula for the Present Value of an Annuity. Assume the interest rate is 4%.

You will need a financial calculator to perform this calculation. Online financial calculators can be downloaded for free from a number of sites, such as

To calculate the answer using a financial calculator, input the interest rate (4%), the number of time periods (15 years) and the payment amount ($60,000).  You should obtain a present value of $667,103.25.

If you do not have a financial calculator, you can consult an annuity table, which sets forth the pre-calculated compound interest rates for each period of years at each basic interest rate. Annuity tables are widely published and widely available online (See, for example, the table published at A typical annuity table depicts the years running down the first column and the rates of interest running across the top row. By finding 15 years on the first column and 4% on the top row, and drawing the points together, you can obtain a pre-calculated compound interest rate of 11.1184.  This rate should then be multiplied times the payment amount.  In the example above, we would multiple 11.1184 times $60,000 which yields a present value of $667,104 (nearly exactly the same result as using a financial calculator).

What this means is that you should not accept less than $667,104 today in lottery proceeds in exchange for passing up the annuity payments of $60,000 for the next 15 years.

Let’s try another application of the formula for a Present Value of an Annuity.  Assume that an insurance carrier has offered $600,000 to settle a lawsuit or, as an alternative, a yearly payment of $45,000 over 20 years. Assume the interest rate is 3%. Which is the best alternative – the lump sum payment of $600,000 or the 20 annual payments of $45,000?

To arrive at the answer, we need to know the present value of 20 annuity payments of $45,000 based on 3% interest. By plugging the interest rate (3%), the number of time periods (20) and the payment amount ($45,000) into a financial calculator, we find that the present value of the annuity is $669,486.37. Or, by using an annuity table, we find that the pre-calculated compound interest rate for 3% over 20 years is 14.8775.  We then multiply 14.8775 times $45,000 to obtain the present value of $669,487.50 (again, quite close to the result obtained by using the financial calculator).

Therefore, we should reject the insurance carrier’s offer of $600,000 to settle the case in a lump sum. The annuity payments have a present value of $669,487.50 and therefore present the better deal. [Or, if the insurance carrier wishes to settle the case today with single lump sum payment, then your bottom line should be greater than $669,487.50].

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