P$6-18($p$.287)$ Bond value and time: Constant required returns Pecos Manufacturing has just issued a $15-$year, $12\%$ coupon rate, $$1,000-$par bond that pays interest annually. The required return is currently $14\%,$ and the company is certain it will remain at $14\%$ until the bond matures in $15$ years.

a$.$ Assuming that the required return does remain at $14\%$ until maturity, find the value of the bond with $(1)15$ years, $(2)12$ years, $(3)9$ years, $(4)6$ years, $(5)3$ years, and $(6)1$ year to maturity.

b$.$ Plot your findings on a set of "time to maturity $(x-$axis$)-$market value of bond $(y$ axis$)"$ axes constructed similarly to Figure $6\mathrm{.}6($p$.274).$

c$.$ All else remaining the same, when the required return differs from the coupon rate and is assumed to be constant to maturity, what happens to them bond value as time moves toward maturity? Explain your answer in light of the graph in part b$.$