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A three-year bond has a par value of $100, a coupon rate of 7% and a yield to maturity of 5%

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A three-year bond has a par value of $100, a coupon rate of 7% and a yield to maturity of 5%. All coupons are paid annually. A five year zero coupon bond is also available with a yield to maturity of 6% and par value of $1,000.

a. Calculate the duration of the bond.

b. Suppose you wish to create a portfolio worth $1,000,000 and with a duration of 4 years, consisting of the three-year coupon bond and the five-year zero-coupon bond. How much money should be invested in each type of bond?