Question

The British government has an outstanding perpetual bond (aka "consol") paying $100 per month forever. Assuming an effective annual rate (EAR) of 4.0742%, the value of the bond immediately before a payment is made is closest to ________.

a. $29,453
b. $30,100
c. $30,000
d. $29,553

Answer 1

The value of the bond immediately before a payment is made can be calculated using the formula for the present value of a perpetuity.

The value of the bond immediately before a payment is made can be calculated using the formula for the present value of a perpetuity. In this case, the annual cash flow is $100 and the effective annual rate (EAR) is 4.0742%. The formula for the present value of a perpetuity is:

PV = CF / r

Where PV is the present value, CF is the cash flow, and r is the interest rate as a decimal. Plugging in the values, we get:

PV = $100 / 0.040742 = $2,453.53

Therefore, the value of the bond immediately before a payment is made is closest to $2,453.53.