Suppose you purchase a $15-$year Treasury bond with a $5\%$ annual$$ coupon, initially trading at par. In $8$years$\text{'}$ time, the$$ bond's yield to maturity has risen to $7\%($EAR$).($Assume $$$$100$ face value$$ bond.$)$

a$.$ If you sell the bond$$ now, what internal rate of return will you have earned on your investment in the$$ bond?

b$.$ If instead you hold the bond to$$ maturity, what internal rate of return will you earn on your initial investment in the$$ bond?

c$.$ Is comparing the IRRs in $($a$)$ versus $($b$)$ a useful way to evaluate the decision to sell the$$ bond? Explain.