The Problem:

You win the grand prize on a game show. You have the following choices:

Option $1$: $$1-$million dollars paid as a $$25000$ annuity every year over $40$ years.

Option $2$: The present value of option $1$ if the current interest rate is $4\%,$ compounded annually. If you accept this option you receive the entire amount immediately, in one payment.

You accept Option $2,$ and invest your prize money with your own bank, in an annuity that will still pay you $$25,000$ every year. Your bank offers you $5\%$ interest, compounded annually. Over $40$ years how much more money would you have earned than if you accepted Option $1?$