Assume a $$1,000$ face value bond has a coupon rate of $8\mathrm{.}5$ percent, pays interest semi$-$annually, and has an eight$-$year life. If investors are willing to accept a $10$ percent rate of return on bonds of similar quality, what is the present value or worth of this bond?

See Problem $4$ to answer these two questions.

a$.$ By how much would the value of the bond in Problem $4$ change if investors wanted an $8$ percent rate of return?

b$.$ A bond with the same par value and coupon rate as the bond in Problem $4$ has $14$ years until maturity. If investors will use a $10$ percent discount rate to value this bond, by how much should its price differ from the bond in Problem $4?$