An insurance company is analyzing the following three bonds, each with five years to maturity, annual interest payments, and the yield is $10\%.$ Assume par value is $$1,000.$ You compute the

duration of each bond with:

a$.$ coupon rate $=8\%$

b$.$ coupon rate $=10\%$

c$.$ coupon rate $=12\%$

What can be inferred from your findings regarding the connection between duration and coupon rate? Generate a graph illustrating this relationship, with duration plotted on the Y$-$axis and coupon rate on the X$-$axis.