An insurance company has a liability of $750,000$ due four years from now. To

protect against interest rate risk, it decides to employ the technique of full

immunization. Specifically, it decides to hold three assets, each providing a single

cash flow as follows:

$($i$)$ Asset $x$ provides a cash flow of $A_x,$ exactly two years from now.

$($ii$)$ Asset Y provides a cash flow of $250,000,$ exactly four years from now.

$($iii$)$ Asset $Z$ provides a cash flow of $A_Z,$ exactly five years from now.

The annual discount factor is $v=0\mathrm{.}95.$

Calculate $A_x$

$150,000$

$175,000$

$200,000$

$225,000$

$250,000$