kathryn harper and her husband, Winston, were beside themselves one weekend in early November.

The 63-year-old Salem grandmother had just scratched a $5 Massachusetts State Lottery ticket and discovered she was an instant millionaire, giving the couple money they could use to make trips, help their kids, and pay off their mortgage for a worry-free retirement.

The Harpers pondered over the weekend about what to do, whether to take the $650,000 cash option or select 20 annual payments of $50,000 before taxes. They chose the payout up front, giving them a check for about $455,000 after taxes were paid.

“We’re not young enough that the [annuity] would have done us any good,” says Kathryn Harper, a carpenter at the Westin Copley Place hotel in Boston where she has worked for more than 26 years. “It just wouldn’t do what we wanted it to do.”

What few people realize is that the Lottery saves money every time a winner chooses the cash payout.

In Harper’s case, the bond needed to fund 20 annual payments totaling $1 million would have cost the Lottery about $715,000. By choosing the $650,000 cash payout, Harper saved the Lottery about $65,000.

“That’s very interesting,” says Harper, who said she was told by Lottery officials that her cash payout was the same as what a $1 million bond would have cost. “I guess you could argue we should have gotten that extra money.”

Lottery officials introduced the $650,000 cash payout for prizes of $1 million or more in June 2009. Prior to that, winners only had the option of taking 20 annual payments.

Lottery spokesman Dan Rosenfeld says officials were finding that many winners were selling their annuities for $500,000 or less to unscrupulous companies who would collect the remaining checks at a healthy profit.

“A lot of our players were looking for a cash option,” says Rosenfeld. “We added that to the prize mix so the players could have a choice. It’s been pretty popular. Our players were not doing very well on the open market.”

When the $650,000 cash payout figure was selected, the cost of purchasing a federal bond to cover an annuity worth $1 million was about $680,000, but the cost has risen since then. That means winners who choose the cash option put a little extra cash in the Lottery’s pocket—at least an estimated $2.7 million so far.

Lottery officials say the winners are still doing better financially than they did before when they sold their annuities on the open market. “We do have a savings,” says Rosenfeld. “But the person is making $150,000 more with our offering.”

Similar payout confusion arises with the big game drawings and their multimillion dollar jackpots. For instance, the multi-state Mega Millions game advertised a jackpot in December of $145 million with a cash payout of $91.8 million. Only the cash payout was guaranteed, however. The larger payment of $145 million —an annuity spread over 26 annual checks—would have become reality only if the cost of purchasing the bond equaled $91.8 million, the size of the cash payout. If it didn’t, the states bankrolling the Mega Millions game would only purchase whatever the $91.8 million would buy and the winner would have to accept that.

The high finance of the Lottery is intriguing to Harper, but she’s not losing any sleep over it. She says she would have liked to increase her winnings by $65,000, but the $650,000 payout on her $5 ticket was still a very good return. “It’s a lot, a lot of money,” she says.