Question: A pension fund must make two fixed payments (2 liabilities): a first payment of $300 due in 5 years and a second payment of $750

A pension fund must make two fixed payments (2 liabilities): a first payment of $300 due in 5 years and a second payment of $750 due in 10 years. The current market interest rate is 3% at all maturities. The fund has $1,000 available to invest today. The fund can allocate its assets between 5-year zero-coupon notes and 20-year zero-coupon bonds. Each bond and note has a face value of $1. The fund wants to stabilize its equity/assets ratio. What is the initial equity value of the fund? Furthermore what is the duration of the liability and what percent of the market value of assets should be invested in the 20-year bond? Give an answer out to two decimal places.

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