In 1752, the British government converted all of its outstanding bonds to perpetual bonds that paid a fixed interest rate. These bonds paid only the interest every three months—the principal amount of the debt would never be repaid. The perpetual bonds have come to be known as “Consols,” and they trade in the British financial markets. The owner of a £1000 face-value (or denomination) Consol receives £6.25 every three months.
a. What is the fixed interest rate (on the face value) paid by the Consols?
b. If the prevailing long-term interest rate in the British financial markets is 4.5% compounded quarterly, what is the fair market value of a £1000 face-value Consol? (Assume that you will receive the first interest payment in three months.)