I need to rate the following bonds from most price risk to low price risk. IF the interest rate increases by 1%

10 year bond 5%

10 year bond zero coupon

5 year bond 5%

5 year bond 10 %

My answer is

10 years zero coupon

10 year 5%

5 year 10%

5 Year 5%

I thought because zero coupon doesn't pay any interest out, but it still could be affected because rising interest isn't good for bonds

thanks