An insurance company accepts an obligation to pay $10,000 at the end of year 1, $15,000 at the end of year 2, and $20,000 at the end of year 3. The insurance company purchases a combination of the following three bonds at a total cost of X in order to match its obligation:
(1) 1-year 3% annual coupon bond with a yield of 5%
(2) 2-year 4% annual coupon bond with yield of 5%
(3) 3-year 6% annual coupon bond with yield of 5%
Compute X