Assume that all interest rates in the economy decline from $10\%$ to $9\%.$ Which of the following bonds would have the largest percentage increase in price?

a$.$ An $8-$year bond with a $9\%$ coupon.

b$.$ A $1-$year bond with a $15\%$ coupon.

c$.$ A $3-$year bond with a $10\%$ coupon.

d$.$ A $10-$year zero coupon bond.

e$.$ A $10-$year bond with a $10\%$ coupon.

For example i know the first one $($A$)$ is a $946$ for the $10\%$ and then $1000$ for the $9\%$ but then my teacher gets a $5\mathrm{.}7\%$ number from those two can you please explain how he got the $5\mathrm{.}7\%$ as well