A $10-$year Treasury bond has a $12\%$ annual coupon, the $15-$year T$-$bond has an annual $8\%$ coupon, the yield curve is flat, and all treasury securities have a $10\%$ yield to maturity. Which of the following statements would be accurate?

Question $11$ options:

a$)$

If interest rates decline, the prices of both bonds will increase with the $15-$year bond having a larger percentage increase in price.

b$)$

If the yield to maturity for both bonds remains steady 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.

c$)$

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

d$)$

The prices of both bonds will increase if interest rates decline with the $10-$year bond having a larger percentage increase in price.