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My pension plan will pay me $$15,000$ at the end of each year for" the next $2$ years. The current interest rate is $10\%$ per year. The pension fund wants to fully immunize its position by purchasing zero$-$coupon bond. What should be the maturity of the zero$-$coupon bond? How many zero$-$coupon bonds the pension fund should purchase if the par value for one bond is $$1000?$