please show work

1. Consider a 2-year, risk-free bond with a coupon rate of 6% (annual coupons) and a face amount of $1,000. a. What is price of this bond if the YTM is 5%? 6% 7%? b. What is the YTM if the price is $980? $1,000 $1,020? c. If you buy the bond for $980, hold it to maturity and you reinvest the coupon payment at 6%, what is the annualized HPR on your investment? d. If you buy the bond for $1,000 (YTM = 6%), then the yield increases to 7%, and you sell the bond immediately after the first coupon payment, what is your HPR? e. You buy the bond for $1,000 (YTM=6%), then the yield increases to 7%, and you sell the bond immediately after the first coupon payment. If you take the proceeds from the sale plus the coupon payment and buy a l-year, zero-coupon bond with a yield of 7%, what is your annualized HPR over the 2-year period