A railroad company is required to pay $79,860 with a modified duration 2.73. The company invests $15,000

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Question:

A railroad company is required to pay $79,860 with a modified duration 2.73. The company invests $15,000 in a bond with modified duration 1.80, and $45,000 in a bond with modified duration X, to immunize its position against small changes in the yield rate. The annual effective yield rate for each of the bonds is 10%.

Calculate X.