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The British government has a consol bond outstanding paying pound £300 per year forever. Assume the current interest rate is 8% per year. a.  What is the value of the bond immediately after a payment is​ made? b.  What is the value of the bond immediately before a payment is​ made?

Question

The British government has a consol bond outstanding paying pound £300 per year forever. Assume the current interest rate is 8% per year. a.  What is the value of the bond immediately after a payment is​ made? b.  What is the value of the bond immediately before a payment is​ made?

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Solution

a. The value of a perpetuity (a bond that pays forever) can be calculated using the formula:

Value = Payment / Interest Rate

In this case, the payment is £300 and the interest rate is 8% (or 0.08 in decimal form). So, the value of the bond immediately after a payment is made would be:

Value = £300 / 0.08 = £3750

b. The value of the bond immediately before a payment is made is the same as the value immediately after a payment is made, because the payment does not affect the value of the perpetuity. Therefore, the value of the bond immediately before a payment is also £3750.

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