8. The demand for one-year discount bonds with a $1000 face value is given by P

Question

8. The demand for one-year discount bonds with a $1000 face value is given by P 1000- 2B, where Pis the bond price and B is the number of the bonds demanded. The supply of the bonds is given by P- 700+ 3B. Find the equilibrium o-38 70+38 a. price of the bond P b. quantity B* of the bonds bought & sold; c. interest rate (yield to maturity) i*. The Bank of Canada has decided to sell 10 more bonds with a $1000 face value at whatever price the market pays, in the market described in question 8 above. Find the equilibrium 9. a. b. c. price of the bond P*; quantity B* of the bonds bought& sold; interest rate (yield to maturity)

Explanation / Answer

Question 8

Demand function of bonds -

P = 1,000 - 2B

Supply function of bonds -

P = 700 + 3B

Equilibrium is attained when demand equals supply

Equating demand and supply functions,

1,000 - 2B = 700 + 3B

5B = 300

B = 300/5 = 60

Value of B can be put in either demand function or supply function to determine the price.

P = 1,000 - 2B

P = 1,000 - (2*60) = 1,000 - 120 = 880

Thus,

The price of bond P* is $880.

(b)

The quantity Q* of the bonds bought and sold is 60 bonds.

(c)

Calculate the interest rate (yield to maturity) i* -

Yield to maturity = [(Face value of bond - Current price of bond)]/Current price of bond

Yield to maturity = ($1,000 - $880)/$880 = 0.1364 or 13.64%

Thus,

Interest rate (Yield to maturity) i* is 13.64%.

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