Question

The demand curve and supply curve for one-year (matures in one year) discount bonds (C=0) with a face value of $1,000 are represented by the following equations: Demand: Qd = 1900 -1.7P where Qd is quantity demanded and P is price Supply: Qs = -750 + 1.0P where Qs is quantity supplied and P is price.

a. What is the equilibrium price and quantity of bonds in this market? Show your work

b. Given your answer to part (a), what is the interest rate for this bond? Show your work.

Answer 1

Bond face value = 1000 $

Time = 1 Year

Demand Od = 1900 - 1.7P

Supply Qs = -750 + 1P

a. Equilibrium will takes place where Qd = Qs

1900 - 1.7P = -750 + 1P

2650 = 2.7P

Equilibrium Price = 981.48 $

Equilibrium Quantity Qd = 1900 – 1.7P

= 1900 – 1.7(981.48)

= 231.484

b. Bond interest rate = (Future value / Present bond Price)^(1 / Years to maturity)    - 1

= (1000 / 981.48)^(1 / 1)    - 1

= 1.0188694624444716142967762970208   - 1

= 1.886 %