$1.(2$ points$)$ Please include your answer and your explanations for the following questions:

a$.$ Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate?

b$.$ Suppose today a $10$ percent coupon bond sells at par. Two years from now, the required return on the same bond is $8$ percent. What is the coupon rate on the bond now? What is the YTM$?$

$2.(1$ point$)$ Companies pay rating agencies such as Moody$$s and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it$?$

$3.(1$ point$)$Most corporate bonds in the United States make coupon payments semiannually, but bonds issued elsewhere often have annual coupon payments.

Suppose a German company issues a bond with a par value of $1,000,20$ years to maturity, and a coupon rate of $4$ percent paid annually. If the YTM is $3\mathrm{.}2$ percent, what is the current bond price in euros?

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$4.(1$ point$)$ Company A issued $25-$year bonds two years ago at a coupon rate of $5\mathrm{.}6$ percent and a face value of $$1000.$ The bonds make semiannual payments.

a$.$ If these bonds currently sell for $97$ percent of face value, what is the YTM$?$

b$.$ If these bonds currently sell for $$1120,$ What is the current yield of the bond?

$5.(2$ points$)$ Bond J has a coupon rate of $3$ percent. Bond K has a coupon rate of $9$ percent. Both bonds have $18$ years to maturity, make semiannual payments, have a face value of $$1000$ and a YTM of $6$ percent.

a$.$ If interest rates suddenly rise by $2$ percent, what is the percentage price change of these bonds? What if rates suddenly fall by $2$ percent instead? $($Hint: $\%$ price change $=100\%*($new price $$ old price$)/$old price$)$

b$.$ What does this problem tell you about the interest rate risk of lower$-$coupon bonds?