Lottery vs. annuity: required rate of return for retirement

Q. at what required rate of return are you indifferent between a $250,000 lump sum payment or a lifetime annuity of $51,200? You will live for 15 years after retirement.

I think this has to be done thru trial and error and I arrived at 24.8% as the answer which makes both the lump sum and the annuity the same amount after 15 years, but my instructor deducted 4 points with no explanation. Should I have figured out what interest rate $51,200 needs to turn into $250,000 after 15 years instead and just assumed I wouldn't earn any interest on the $250,000?

Re: Lottery vs. annuity

This is a horribly defined question.

1) When is retirement? Did you assume it was immediately? It's not in the problem statement as presented.

2) What is the nature of the annuity payments? Annual? Semi-Annual? Monthly?

Anyway, if you did assume retirement was immediately and payments were annual, starting immediately, you should have gotten 24.565%. You're a little high.