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Company FM2 must pay 1,000,000 in x years. In order to fully immunize from changes in interest rate, the company invests in a zero coupon

Company FM2 must pay 1,000,000 in x years. In order to fully immunize from changes in interest rate, the company invests in a zero coupon bond that matures for 491,833 in x 3 years. Also, the company can invest in a zero coupon bond that matures for 523,458 in x + t years. The actuary for Company FM2 determined that their portfolio fully immunized their ability to meet their obligations at the current constant force of interest of 5%.

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