Leland Price must pay $5,000 for six months from now and $10,000 one year from n

Question

Leland Price must pay $5,000 for six months from now and $10,000 one year from now. He wishes to purchase bonds so that together they form a portfolio of assets that exactly match his liabilities. Available bond are six-months zero-coupon $1,000bond that has a 3.0225% annual yield, and a one-year $1,000 par-value 6% bond with semiannual coupons and a 4% nominal yield (convertible semiannually). How much must Leland pay to purchase the bonds? Assume that he may buy any quantity he wishes of each bond.

So I have solved this problem and am reworking it. Where I am stuck is on the six month bond to calculate its price I used an interest of 1.51125%. I cannot figure out how I got that from the 3.0225%

I am stuck on how to convert the interest rate from an annual to a six month one.

Below is my work

Explanation / Answer

Present Value of 6-month zero-coupon bond = 1000/(1+1.51125%) = 985.1125

(Your assumption is right 1.51125% is calculated by converting the annual yield 3.0225% to semiannual, by dividing it by 2)

Present Value of 1 year bond =1000*2%/(1+3%)+1000*2%/(1+3%)^2+1000/(1+3%)^2 = 980.8653

So, to meet his future liabilities, Leland Price needs to purchase bonds for 5*985.1125 + 10*980.8653 = $ 14,734.22

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