A manager of a commercial bank$$s security portfolio is analyzing three bonds and is using duration as the measure of interest rate risk. The three bonds all trade at a yield to maturity of $10$ percent and have $$10,000$ par values. The bonds differ only in the amount of annual coupon interest that they pay: $8,10,$ or $12$ percent.

a$.$ What is the duration for each five$-$year bond?

b$.$ What is the relationship between duration and the amount of coupon interest that is paid?