A perpetuity is an annuity in which the periodic payments begin on a fixed date and continue indefinitely. It is sometimes referred to as a perpetual annuity. Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. Scholarships paid perpetually from an endowment fit the definition of perpetuity.

The value of the perpetuity is finite because receipts that are anticipated far in the future have extremely low present value (present value of the future cash flows). Unlike a typical bond, because the principal is never repaid, there is no present value for the principal. Assuming that payments begin at the end of the current period, the price of a perpetuity is simply the coupon amount over the appropriate discount rate or yield, that is PV = A over V

Where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield, discount rate or interest rate.

To give a numerical example, a three per cent UK government War Loan will trade at 50 pence per pound in a yield environment of six per cent, while at three per cent yield it is trading at par. That is, if the face value of the Loan is £100 and the annual payment £3, the value of the Loan is £50 when market interest rates are six per cent, and £100 when they are three per cent.

For example, UK government bonds, called consols, that are undated and irredeemable (e.g. War loan) pay fixed coupons (interest payments) and trade actively in the bond market. Very long dated bonds have financial characteristics that can appeal to some investors and in some circumstances, e.g. Long-dated bonds have prices that change rapidly (either up or down) when yields change (fall or rise) in the financial markets.

The value of the perpetuity is finite because receipts that are anticipated far in the future have extremely low present value (present value of the future cash flows). Unlike a typical bond, because the principal is never repaid, there is no present value for the principal. Assuming that payments begin at the end of the current period, the price of a perpetuity is simply the coupon amount over the appropriate discount rate or yield, that is PV = A over V

Where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield, discount rate or interest rate.

To give a numerical example, a three per cent UK government War Loan will trade at 50 pence per pound in a yield environment of six per cent, while at three per cent yield it is trading at par. That is, if the face value of the Loan is £100 and the annual payment £3, the value of the Loan is £50 when market interest rates are six per cent, and £100 when they are three per cent.

For example, UK government bonds, called consols, that are undated and irredeemable (e.g. War loan) pay fixed coupons (interest payments) and trade actively in the bond market. Very long dated bonds have financial characteristics that can appeal to some investors and in some circumstances, e.g. Long-dated bonds have prices that change rapidly (either up or down) when yields change (fall or rise) in the financial markets.