In: Finance
An insurance company accepts an obligation to pay $7,000 at the end year 1, pay $8,000 at the end of year 2, and pay $9,600 at the end of year 3. The insurance company purchases a combination of the following three bonds in order to exactly match its obligation.
• Bond 1: 1-year 6% annual coupon bond with yield rate of 8%.
• Bond 2: 2-year zero coupon bond with yield rate of 7%.
• Bond 3: 3-year 20% annual coupon bond with yield rate of 12%.
(a) What face amount of each bond should the insurance company buy to do this?
(b) What price should the insurance company pay for the 3-year bond?
Please show detailed steps, and please don't use excel. I want to understand this.