Assume all rates are annualized with semi-annual compounding. Please be explicit about how you derive your results and round to four decimals after the comma. The 0.5-year zero rate is 7% and the 1-year zero rate is 9%.

a. What is the duration of: i. $1 par of a 0.5-year zero? ii. $1 par of a 1-year zero? iii. $100 par of a 1-year 10%-coupon bond? b Use dollar duration to estimate the change in value of $1,000 par of the 1-year 10%- coupon bond if all zero rates rise 100 basis points.