Question

Imagine that the government decided to fund its current deficit of \$431$431 billion dollars by issuing a perpetuity offering a 4\%4% annual return. How much would the government have to pay bondholders each year in perpetuity? Express your answer in billions of dollars.

(Hint: The \$431$431 billion is just the present value of these cash flows at a discount rate of 4\%4%.)

Answer 1

Given:

The government has a current deficit of = $ 431 billion dollars

The annual rate of return = 4%

To find:

The amount that the government have to pay bondholders each year in perpetuity (in terms of billions of dollars)

Solution:

We know that, the current deficit of $ 431 billion dollars is the present value of the cash flows or perpetuity.

So, to find the periodic cash payment made on an annual basis, we will use the following formula,

$\boxed{\bold{Present\:Value\: of \:Perpetuity\:=\:\frac{Periodic \:Cash \:Payment}{Interest\:or\:Discount\:Rate} }}$

We will now substitute the given values in the above formula,

$\ 431 \:billion\: dollars = \frac{Annual\: Cash\: Payment}{4\% }$

⇒ $\ 431 \:billion\: dollars = \frac{Annual\: Cash\: Payment}{\frac{4}{100}}$

⇒ $Annual\: Cash\: Payment = [\ 431 \:billion\: dollars] * \frac{4}{100}$

⇒ $Annual\: Cash\: Payment = \frac{\ 1724 \:billion\: dollars}{100}$

⇒ $Annual\: Cash\: Payment = \ 17.24 \:billion\: dollars$

Thus, the government would have to pay bondholders $ 17.24 billion dollars each year in perpetuity.

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