Sam is obligated to pay 10000 in 6 months 15000 in 12 months and $25000 in 18 months he wishes to purchase bonds to exactly match these liabilities (dedication) the bonds available for purchase by sam are the following 3 types:

a)6 month zero coupon bonds

b) 12 month 6% par value bonds with semiannual coupons

c)18 month 5% par value bonds with semi annual coupons.

Assume that each bond may be purchases for any par value Sam would like. How much of each of these bonds should Sam Purchase?

Answers: $8971.11 of 6-month bond, $13,971.11 of 12-month bond, $24390.24 of 18-month bond.

Need help finding the formulas to get the answers.