Bond value and time$-$Constant required returns Pecos Manufacturing has just issued a $15-$year, $12\%$ coupon interest 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, $(6)1$ year to maturity.

b$.$ All else remaining the same, when the required return differs from the coupon interest rate and is assumed to be constant to maturity, what happens to the bond value as time moves toward maturity?

Explain in light of the following graph:

a$.(1)$ The value of the bond with $15$ years to maturity is $$877\mathrm{.}16.($Round to the nearest cent.$)$

$(2)$ The value of the bond with $12$ years to maturity is $ $($Round to the nearest cent.$)$