By using Eq. (3.33) and taking the limit for \(T+\), it is easy to find the price of a perpetuity, i.e., an annuity where \(T+\), paying an annual amount \(C\), which may be thought as a fraction \(c\) of a virtual nominal \(F\) :

The notation suggests the interpretation of this security as a couponbearing bond with infinite maturity. For instance, if \(y_{1}=5 \%\) and \(C=10\) 000, we have

 

Note that \(5 \%\) of this value is exactly the annual payment, i.e., what is required to pay the annual coupon while keeping the capital intact, assuming that it will be reinvested at a rate forever. Given the stochastic nature of interest rates, this will be hardly the case.

Data From Equation 3.33

Transcribed Image Text:

Pe(0, 0) = C Y1