$1.$ Consider the following two bonds:

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Bond A

Bond B

Face value

$$1,000$

$$1,000$

Coupon rate $($annual$)$

$8\%$

$8\%$

YTM

$9\%$

$7\%$

Maturity

$10$ years

$10$ years

Price $($PV$)$

$?$

$?$

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Calculate the price for each bond. What is the primary factor affecting the prices of the bonds? Indicate which bond is premium and which one is discount. Is there any relationship between the YTM and the coupon rate in case of premium$/$discount bonds?

Now, consider the following two bonds:

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Bond X

Bond Y

Face value

$$1,000$

$$1,000$

Coupon rate $($annual$)$

$8\%$

$8\%$

YTM

$11\%$

$11\%$

Maturity

$5$ years

$10$ years

Price $($PV$)$

$?$

$?$

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Calculate the price for each bond. What is the relationship between bond price and maturity, all else equal?

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$2.$ A bond with a par value of $$1,000$ and a maturity of $8$ years is selling for $$925.$ If the annual coupon rate is $7\%,$ what$$s the yield on the bond? What would be the yield if the bond had semiannual payments?

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$3.$ A bond has a par value of $$1,000,$ a time to maturity of $8$ years, and a coupon rate of $10\%$ with interest paid annually. If the current market price is $$875,$ what will be the approximate price of this bond at the end of the first year?

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$4.$ A $15-$year maturity, $8\%$ coupon bond paying coupons semiannually is callable in $7$ years at a call price of $$1,050.$ The bond currently sells at a yield to maturity of $9\%$ per year.

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a$.$ What is the yield to call?

b$.$ What is the yield to call if the call price is $$1,100$ and the bond can be called in $3$ years instead of $7$ years?

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$5.$ A bond with a $10\%$ coupon paid semiannually every January $15$ and July $15$ is quoted as selling at an ask price of $$1,012\mathrm{.}5.$ If you buy the bond from the dealer today $($check the date!$),$ what price will you pay for it$?$ What price will you pay for the bond if the coupons are paid quarterly? $[$You need to calculate the accrued interest in both cases to calculate the invoice price$].$