A corporate bond matures in 2 years, pays semi-annual coupons, has a coupon rate of 6.4% and a AA credit rating. A 2-year Treasury bond that makes payments on the same days as the corporate bond has a yield to maturity of 1.8% (APR, semiannual compounding). The credit spread on AA bonds is 90 basis points (0.90%). What should be the price of the corporate bond? Assume a $1,000 face value.

Answer: $1,071.57. Please show how to arrive to this answer.