An insurance company has a single liability due in three years. The company fully immunizes its position by purchasing one$-$year and

four$-$year zero$-$coupon bonds. The face value of the one$-$year bond is $20,000$ and the face value of the four$-$year bond is $50,000.$

Assume that the yield curve is flat.

Calculate the amount of the liability.

$40,000$

$55,699$

$69,624$

$73,333$

$97,500$