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A corporate pension plan has to make the following payments over the next few years: Year...

A corporate pension plan has to make the following payments over the next few years:

Year 1 2 3 4
Amount ($ million) 27 31 37 45

The appropriate interest rate is 7%.

What is the present value of the liability (in $ million)?

What is the duration of the liability?

What is the duration of a perpetuity if the yield is 7%?

The fund wants to immunize its interest rate risk by investing in a perpetuity and a 1-year zero coupon bond. To do so, how much should it invest in the perpetuity (in $ million)?

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