You are an actuary for an insurance company that has an obligation to pay $ 10,000 every year for 5 years. Your company accepts payments of $ 37,908, i.e. the present value of the obligation with an interest rate of 10% and will use it for investment so obligations fulfilled. The investment available for your company is zero-coupon bonds 1, 3, and 5 years all of which give a 10% yield. Your job is to create an investment strategy for your company using classical immunization, only consider adjusting the duration of assets and liabilities without consider convexity. It is known that your company is investing in a 1-year zero-coupon bond in the amount of $ 13,223. Determine the amount of investment in zero-coupon bonds 3 years and 5 years.

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