A firm issued a new series of bonds on January 1, 1992. The bonds were sold at par ($1,000), have a 12 percent coupon, and mature in thirty years. Coupon payments are made semi-annually (on June 30 and December 31). a. What was the yield to maturity of the bond on 1/1/92? b. Calculate the price of the bond on 1/1/97, five years later, assuming that the level of interest rates have fallen to 10 percent. c. If, on July 1, 2012, an investor expects the bonds to sell for $896.64. What is the expected yield to maturity on the bonds at that date?

a. The yield to maturity of the bond on 1/1/92 was 12 percent. This is because the bond was sold at par value, which means the yield to maturity is equal to the coupon rate.

b. To calculate the price of the bond on 1/1/97, we need to calculate the present value of the future cash flows, which are the semi-annual coupon payments and the face value of the bond at maturity. The formula for the price of a bond is:

P = C * (1 - (1 + r/n) ^ -nt) / (r/n) + F / (1 + r/n) ^ nt

where: P = price of the bond C = semi-annual coupon payment = $1,000 * 12$60 r = annual interest rate = 10% n = number of compounding periods per year = 2 t = number of years until maturity = 30 - 5 = 25 F = face value of the bond = $1,000

Substituting these values into the formula, we get:

P = $60 * (1 - (1 + 10$1,000 / (1 + 10%/2) ^ 2*25 P = $60 * (1 - 0.61391) / 0.05 +$1,000 / 0.61391 P = $60 * 7.72 +$1,629.41 P = $1,093.20

So, the price of the bond on 1/1/97 was approximately $1,093.20.

c. If, on July 1, 2012, an investor expects the bonds to sell for $896.64, the expected yield to maturity can be calculated using the formula for the yield to maturity of a bond, which is:

r = 2 * [ (C * (t + 1) + (F - P) / t) / (F + P) ]

where: r = yield to maturity C = semi-annual coupon payment = $60 t = number of semi-annual periods until maturity = (30 - 20.5) * 2 = 19 F = face value of the bond =$1,000 P = price of the bond = $896.64

Substituting these values into the formula, we get:

r = 2 * [ ($60 * (19 + 1) + ($1,000 - $896.64) / 19) / ($1,000 + $896.64) ] r = 2 * [ ($60 * 20 + $103.36 / 19) /$1,896.64 ] r = 2 * [ $1,200 +$5.44 / $1,896.64 ] r = 2 * [$1,205.44 / $1,896.64 ] r = 2 * 0.635 r = 1.27

So, the expected yield to maturity on the bonds on July 1, 2012, was approximately 1.27 percent.