Suppose the following annuity is payable to a life now aged x:

If (x) is alive at the end of the first year, $1,000 will be paid.

If (x) is alive at the end of the second year, $3,000 will be paid.

If (x) is alive at the end of the fourth year, $6,000 will be paid.

Find an expression for the expected present value of the annuity, and evaluate it assuming x = 30, interest is 8% per annum and mortality follows the A1967-70 select table.