$1)$ Explain the different types of value.

$2)$ A bond with a $$1,000$ face value and a $10$ percent annual coupon rate matures in $15$ years.

a$.$ Determine the value of the bond to a friend of yours with a required rate of return of $13\%.$

b$.$ A zero$-$coupon bond with similar risk is selling for $$180.$ The bond has a face value of $$1,000$ and matures in $15$ years. Your friend asks you which bond she should invest in$,$ the zero$-$coupon bond or the bond in part $($a$).$ Which bond do you recommend, and why? Assume the market price of the bond in part $($a$)$ is $$820.$

$3)$ GAT, Inc. has issued a $$1,000$ par $4\%$ annual coupon bond that is to mature in $18$ years. If your required rate of return is $6\mathrm{.}5\%,$ what price would you be willing to pay for the bond?

$4)$ FYI bonds have a par value of $$1,000.$ The bonds pay $$40$ in interest every six months and will mature in $10$ years.

a$.$ Calculate the price if the yield to maturity on the bonds is $7,8,$ and $9$ percent, respectively.

b$.$ Explain the impact on price if the required rate of return decreases.

c$.$ Compute the coupon rate on the bonds. How does the relationship between the coupon rate and the yield to maturity determine how a bond's price will compare to it par value?

$5)$ Graystone bonds have a maturity value of $$1,000.$ The bonds carry a coupon rate of $12$ percent. Interest is paid semiannually. The bonds will mature in nine years. If the current market price is $$976\mathrm{.}50,$

a$.$ what is the yield to maturity on the bond?

b$.$ what is the current yield on the bond?