please show work

1. You have just won a lottery prize. The prize allows you to choose between two alternatives:

   Choice A: Receive a single lump sum of $30,000 at the end of the fourth year. Choice B: Receive a payment of $5,800 at the end of each year for the next four years.

   1. If the interest rate is 10% compounded annually, which alternative has a higher

      present value?

   2. If the interest rate is 20% compounded annually, which alternative has a higher

      present value?