A noncallable $10-$year T$-$bond has a $12\%$ annual coupon, the yield curve is flat, and it has a $10\%$ yield to maturity. A $15-$year noncallable T$-$bond has an $8\%$ annual coupon, the yield curve is flat, and it has a $10\%$ yield to maturity. Which of the following statements is CORRECT?

If interest rates decline, the prices of both bonds would increase, but the $15-$year bond would have a larger percentage increase in price.

If the yield to maturity on both bonds remains at $10\%$ over the next year, the price of the $10-$year bond would increase, but the price of the $15-$year bond would fall.

The $10-$year bond would sell at a premium, while the $15-$year bond would sell at par.

The $10-$year bond would sell at a discount, while the $15-$year bond would sell at a premium.

If interest rates decline, the prices of both bonds would increase, but the $10-$year bond would have a larger percentage increase in price.