You can choose any one of the following prizes. If your discount rate is 10.5% (annual compounding), which is the most valuable prize, i.e. has the greatest present value?

(1) A lump sum payment of $25,000 at the end of 10 years.

(2) A lump sum payment of $10,000 today.

(3) A perpetual stream of annual payments starting at $500 in one year and increasing at 5% per year thereafter.

(4) A perpetual stream of annual payments of $1,000 starting in one year. Five annual payments of $2,800 - the first payment occurs one year from today.