Which of the following statements is CORRECT?

If their maturities and other characteristics were the same, a $5\%$ coupon bond would have more interest rate price risk than a $10\%$ coupon bond.

If their maturities and other characteristics were the same, a $5\%$ coupon bond would have less interest rate price risk than a $10\%$ coupon bond.

A $10-$year coupon bond would have more reinvestment rate risk than a $5-$year coupon bond, but all $10-$year coupon bonds have the same amount of reinvestment rate risk.

A $10-$year coupon bond would have more interest rate price risk than a $5-$year coupon bond, but all $10-$year coupon bonds have the same amount of interest rate price risk.

A zero coupon bond of any maturity will have more interest rate price risk than any coupon bond, even a perpetuity