Consider the following information regarding three annual coupon bonds:

Coupon / Maturity / Price

5% / 1 / $99.06

6% / 2 / $98.19

7% / 3 / $97.42

All bonds have face value of $100.

(e) Consider you have $10,000 to invest in the one-, two- and three-year zero-coupon bonds. You use $3,000 to short the three-year zero-coupon bond. The remaining capital you plan to invest in the one- and two-year zero-coupon bond. How much should you invest in the one-year zero-coupon bond so that your portfolio has no interest rate risk exposure?