Rupert Mannion purchased a yacht which will require a new mast in four years. He is concerned about how much money he will need to put away so that he has enough to cover the cost of the new mast. There is some uncertainty as to the cost of the mast in four years, however, Rupert has found out the following information by consulting yacht manufacturers.

Estimated cost of new mast	Probability Assessment
$400	10%
$900	30%
$1,200	50%
$1,300	10%

If Rupert could earn 3%, compounded annually, how much should he deposit today so that he will have sufficient funds in four years to cover the cost of the new mast? Show all calculations