A bond with $$1,000$ face value, $6\%$ coupon, market interest rates of $\%7,$ and three years to maturity.

a$.$ Calculate the duration of the bond.

b$.$ Assume that market interest rates increased to $10\%,$ re$-$calculate the duration of the bond.

c$.$ Assume that the market interest rates increased to $15\%,$ re$-$calculate the duration of the bond.

d$.$ Comment generally on the relationships between the interest rates, coupons, and duration.