### Lottery Answer

*by James Shapiro*

The question I posed in “Financial Calculation Programs” (April, 1998) is whether it is better to take a single lump sum if you win the lottery or 25 yearly checks. The lump sum is only 40% of your winnings. The first check is for 1/40 of your winnings with the amount increasing by 3.7% each year. The check's total is the promised amount, but you might want to have the lump sum now rather than the full amount distributed over 24 years, especially if you think you can invest it and end up with more money than having the lottery folks do the investing for you. The crucial number in this problem is the effective interest rate or IRR. We need to make a table of amounts and times to input to (any) one of the IRR programs from the article. Let us assume your winnings are one million dollars. If you choose the 25-check option, the first year you are in the hole by $25,000 (the first check) minus $400,000 (the lump sum you forgave for the checks) or $375,000. All the future numbers are positive, however, starting with the check for $25,925 ($25,000 times 1.037) at the end of the first year, up to the last check for $59,790.22 at the end of the 24th year. Our data file looks like this:

-375000.00 0.0
25925.00 1.0
26884.22 2.0
....
57656.92 23.0
59790.22 24.0

Here is a little Perl program which will save you from having to calculate all the check values:
#!/usr/bin/perl
require 5.003;
use strict;
# Colorado lottery example
my($winnings, $f) = (1000000, 1.037);
my $p = $winnings / 40;
foreach (0 .. 24) {
S: {
printf("%.2f %.1f\n",
$p - 0.4 * $winnings, $_),
last if $_ == 0;
printf "%.2f %.1f\n", $p, $_;
}
$p *= $f;
}

If you run this program to generate the dollar,time pairs and input this data into one of the IRR programs, you will get IRR = 8.0141% (discrete) = 7.7091% (continuous) after 4 iterations.
If you can invest the $400,000 lump sum where it will earn more than 7.7% compounded continuously you are better off with the one huge check. Otherwise, you had better (from a strictly financial standpoint) settle for the yearly checks.