Final answer:
To immunize the investment against a change in interest rates and meet the obligation, you would need to purchase approximately $462.47 of the two-year 6% bond with semiannual coupons and $501.456 of the 4-year zero coupon bond.
Step-by-step explanation:
To immunize the investment against a change in interest rates and fully meet the obligation, we need to determine the amount of each bond to purchase. Let's start with the two-year 6% bond with semiannual coupons. The present value of the bond's coupons due at the end of year 3 is calculated using the formula:
PV = C / (1 + r/2)^n
where PV is the present value, C is the coupon amount, r is the yield to maturity, and n is the number of periods. Using a yield of 4.5% and solving for PV, we get:
PV = L / (1 + r/2)^n
Substituting the given values, we have:
1,100 = C / (1 + 0.045/2)^6 + 1,000 / (1 + 0.045/2)^6
Solving this equation, we get the coupon amount C to be approximately $462.47. Since we know the face value of the bond is $1,000, the remaining amount of the liability can be met by purchasing a 4-year zero coupon bond. Using the formula:
Face value = Present value / (1 + r)^n
we can calculate the present value of the zero coupon bond as:
1,100 - 462.47 = PV / (1 + 0.045)^4
Solving for PV, we find that the present value should be approximately $501.456.