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Actuarial FM question: A company must pay a liability of L due one year from now and 2L due two years from now. The company

Actuarial FM question:

A company must pay a liability of L due one year from now and 2L due two years from now. The company exactly (absolutely) matches the liabilities by buying a one-year bond with face value $800 and a two-year bond with face value $2,000. Both bonds have annual coupons, with a coupon rate of r for the one-year bond and 1.25r for the two-year bond. Determine r.

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