An annuity that will continue without time limit (forever) is called a perpetuity. They rarely occur, although sometimes bonds have long maturity periods, such as the recent Walt Disney 100-year bonds.

The equation for a perpetuity of 1 can be expressed as follows:

where

• 1 = the size of the annuity,

• i = the interest rate,

• P = the value of the perpetuity

Then

• P = 1/ i, by simply dividing through by i

Not many perpetuities exist. The most famous were the old British Consols (consolidated loan), which guaranteed interest payments forever, although they were callable at par. The most recent issue was at 2 1/2%, issued in 1888 to refund a previous issue of 3% Consols. Consols are mentioned in many 19 ^th century works of English literature. The Canadian Pacific Railroad and the Canadian National Railroad both also had perpetual 4% outstanding at one time. I know of no American perpetuals, although during the 19 ^th century, one American railroad issued bonds with a maturity year of 2862. In practical terms, this might as well have been a perpetual.