When analyzing a US Treasury note with the following characteristics: $5$ Year maturity, $5\%$ coupon you compare this bond to current interest rates. Current interest rates for a $5-$year US Treasury note is $4\%.$ Given this information, which of the following is NOT true:

You should expect to pay a premium $($more than par$)$ for the bond because the coupon is higher than current interest rates.

You should expect the value of this bond to change less when interest rates change than if you bought the current US Treasury at $4\%$ because the coupon is higher than current interest rate levels.

You should expect the value of this bond to increase if interest rates rise.

You should expect more price volatility in the $5\%$ coupon with a $5-$year maturity than if you bought a $5\%$ coupon treasury with a $3-$year maturity.