A Powerball winner is offered two options:

$1$ lump sum payment of $$177$ million, or $30$ annual payments of $$10\mathrm{.}5$ million $.$

If the average annual interest rate over the term of the payments is $3\mathrm{.}5\%,$ what is the Present Value of the annual payments? $ Round to the nearest dollar.

What is the difference between the lump sum payment and the present value of the annual payments? $ Round to the nearest dollar. Represent as a positive number.

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What if the average annual interest rate over the term of the payments is $7\%,$ what is the Present Value of the annual payments? $ Round to the nearest dollar.

What is the difference between the lump sum payment and the present value of the annual payments? $ Round to the nearest dollar. Represent as a positive number.