Given a series of semi$-$annual coupon$-$paying bonds, all having a coupon rate of $5\%$ and a face value of $$1000.$

When the yield$-$to$-$maturity increases from $7\%$ to $10\%,$ which one of the following bonds will exhibit the smallest decrease in price?

Answer Choices:

a$.$ Bond with $3$ years to maturity

b$.$ Bond with $5$ years to maturity

c$.$ Bond with $20$ years to maturity

d$.$Bond with $10$ years to maturity