Question

**A.** A bond has a par value of $1,000, a time to
maturity of 20 years, and a coupon rate of 7.50% with interest paid
annually. If the current market price is $750, what will be the
approximate capital gain of this bond over the next year if its
yield to maturity remains unchanged? **(Do not round
intermediate calculations. Round your answer to 2 decimal
places.)**

**B.** Suppose that today’s date is April 15. A
bond with a 8% coupon paid semiannually every January 15 and July
15 is listed in *The Wall Street Journal* as selling at an
ask price of 1,020.000. If you buy the bond from a dealer today,
what price will you pay for it? **(Do not round intermediate
calculations. Round your answer to 2 decimal places.)**

Consider a bond paying a coupon rate of 10.50% per year semiannually when the market interest rate is only 4.2% per half-year. The bond has two years until maturity.

Find the bond's price today and six months from now after the
next coupon is paid. **Bonus:** What is the total rate
of return on the bond? **(Do not round intermediate
calculations.** **Round your answer to 2 decimal
places.)**

Answer #1

Ans 1) price of bond = coupon * ( 1 - (1+r)^(-n))/(r) + face value/(1+r)^(n)

where coupon = (7.5% of 1000) = $75

Face value = 1000

n = 20 years

while putting all the values we will get value of r

750 = 75* (1 - (1 + r)^(-20))/r + 1000/(1 + r)^(20)

r = 10.546842

with n = 19

price of bond = 754.10

Capital gain = $4.1

Ans 2) flat price = 1020

accrued interest: (.08*1000)/2 = 40

40*(3/6) = 20

invoice price = 1020 + 20 = $1040

Ans 3) price of bond = coupon * ( 1 - (1+r/2)^(-2n))/(r/2) + face value/(1+r/2)^(2n)

where coupon = (10.5 % of 1000)/2 = $52.5

Face value = 1000

r/2 = 4.2%

n = 2 years

while putting all the values we will get the bond price

= 52.5 * (1 - (1.042)^(-4))/.042 + 1000/(1.042)^(4)

= $ 1037.93

when n = 1.5

price of bond = $1029.03

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