Sandy is obligated to pay $10,000 in six months, $15,000 in twelve months, and $25,000 in eighteen\ months. He wishes to purchase bonds to exactly match these liabilities- that is, to provide inflows\ so that the net cashflo at the three payment times, as well as at all other times, is zero. The bonds\ available for purchase by Sandy are of the following three types:\ Six-month zero-coupon bonds, sold to yield the investor 6% nominal interest convertible semi-\ annually;\ Twelve-month 6% par-value bonds with semiannual coupons;\ Eighteen-month 5% par-value bonds with semiannual coupons.\ How much of each of these should Sandy purchase? Assume that each may be purchased for any\ par value that Sandy would like.