Question

An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $190 annually if the next payment occurs one year from today? The market interest rate is 4.2 percent. (Round your answer to 2 decimal places. (e.g., 32.16)) Present value $

Answer 1

Answer:

               $\large\boxed{\large\boxed{\ 4,523.81}}$

Explanation:

The price of a consol (a type of debt issued by the goverment) is the present value of all the future payments.

A constant payment forever is known as a constant annuity to perpetuity.

The price of a constant perpetuity is calculated with the formula:

      $Price=C/r$

Where C is the constant payment, equal to $190 (annually forever), and r is the opportunity cost, which you assume to be equal to the market interest rate: r = 4.2%.

Substituting:

        $Price=\ 190/(4.2\%) =\ 190/0.042=\ 4,523.81$