A company owes 500 and 1000 to be paid at the end of year one and year four, respectively. The company will set up an investment program to match the duration and the present value of the above obligation using an annual effective interest rate of 10%. The investment program produces asset cash flows of X today and Y in three years.

Calculate X and determine whether the investment program satisfies the conditions for Redington immunization.

• X = 75 and the Redington immunization conditions are not satisfied.
• X = 75 and the Redington immunization conditions are satisfied.
• X = 1138 and the Redington immunization conditions are not satisfied.
• X = 1138 and the Redington immunization conditions are satisfied.
• X = 1414 and the Redington immunization conditions are satisfied.

An insurance company has a known liability of 1,000,000 that is due 8 years from now. The technique of full immunization is to be employed. Asset I will provide a cash flow of 300,000 exactly 6 years from now. Asset II will provide a cash flow of X, exactly y years from now, where y > 8. The annual effective interest rate is 4%.

Calculate X.

• 697,100
• 698,600
• 700,000
• 701,500
• 702,900

A company has liabilities of 573 due at the end of year 2 and 701 due at the end of year 5. A portfolio comprises two zero-coupon bonds, Bond A and Bond B.

Determine which portfolio produces a Redington immunization of the liabilities using an annual effective interest rate of 7.0%.

• Bond A: 1-year, current price 500; Bond B: 6-years, current price 500
• Bond A: 1-year, current price 572; Bond B: 6-years, current price 428
• Bond A: 3-years, current price 182; Bond B: 4-years, current price 1092
• Bond A: 3-years, current price 637; Bond B: 4-years, current price 637
• Bond A: 3.5 years, current price 1000; Bond B: Not used

A company has liabilities of 402.11 due at the end of each of the next three years. The company will invest 1000 today to fund these payouts. The only investments available are one-year and three-year zero-coupon bonds, and the yield curve is flat at a 10% annual effective rate. The company wishes to match the duration of its assets to the duration of its liabilities.

Determine how much the company should invest in each bond.

• 366 in the one-year bond and 634 in the three-year bond.
• 484 in the one-year bond and 516 in the three-year bond.
• 500 in the one-year bond and 500 in the three-year bond.
• 532 in the one-year bond and 468 in the three-year bond.
• 634 in the one-year bond and 366 in the three-year bond.

You are given the following information about a company's liabilities:

• Present value: 9697
• Macaulay duration: 15.24
• Macaulay convexity: 242.47

The company decides to create an investment portfolio by making investments into two of the following three zero-coupon bonds: 5-year, 15-year, and 20-year. The company would like its position to be Redington immunized against small changes in yield rate.

The annual effective yield rate for each of the bonds is 7.5%.

Determine which of the following portfolios the company should create.

• Invest 3077 for the 5-year bond and 6620 for the 20-year bond.
• Invest 6620 for the 5-year bond and 3077 for the 20-year bond.
• Invest 465 for the 15-year bond and 9232 for the 20-year bond.
• Invest 4156 for the 15-year bond and 5541 for the 20-year bond.
• Invest 9232 for the 15-year bond and 465 for the 20-year bond.

An insurance company wants to match liabilities of 25,000 payable in one year and 20,000 payable in two years with specific assets. The following assets are currently available

• One-year bond with an annual coupon of 6.75% at par
• Two-year bond with annual coupons of 4.50% at par
• Two-year zero-coupon bond yielding 5.00% annual effective

Calculate the smallest amount the company needs to disburse today to purchase assets that will exactly match these liabilities.

• 41,220
• 41,390
• 41,560
• 41,660
• 41,750

A company has liabilities that require it to make payments of 1000 at the end of each of the next five years. The only investments available to the company are as follows:

The company is able to purchase as many of each investment as it wants, but only in whole units. The company’s investment objective is to be fully immunized over the next five years.

Calculate the lowest possible cost to achieve this objective.

• 1500
• 2000
• 2500
• 3000
• 4000

A railroad company is required to pay 79,860, which is due three years from now. The company invests 15,000 in a bond with modified duration 1.80, and 45,000 in a bond with modified duration Dmod, to Redington immunize its position against small changes in the yield rate. The annual effective yield rate for each of the bonds is 10%.

Calculate Dmod.

• 2.73
• 3.04
• 3.34
• 3.40
• 3.65

A company must pay liabilities of 1000 at the end of year 1 and X at the end of year 2. The only investments available are:

1. One-year zero-coupon bonds with an annual effective yield of 5%
2. Two-year bonds with a par value of 1000 and 10% annual coupons, with an annual effective yield of 6%

The company constructed a portfolio that creates an exact cash flow matching strategy for these liabilities. The total purchase price of this portfolio is 1783.76.

Calculate the amount invested in the one-year zero-coupon bonds.

• 784
• 831
• 871
• 915
• 935

A company must pay liabilities of 4000 and 6000 at the end of years one and two, respectively. The only investments available to the company are one-year zero-coupon bonds with an annual effective yield of 8% and two-year zero-coupon bonds with an annual effective yield of 11%.

Determine how much the company must invest today to exactly match its liabilities.

• 8,473
• 8,573
• 8,848
• 9,109
• 10,000