Question

what is meant by perpetuity(mathematically and in words) and what type of annuity is perpetuity?

Answer 1

before discussing the concept of perpertuity let's see what is annuity. annuity is a stream of fixed cash flows or payments made at fixed intervals annuity has a fixed ending period.an example for annuity is the insurance contract, in which you pay a lumpsum amount to the insurance company and you get regular disbursement in return.

perpetuity is an annuity with no definite ending period. ie. it is constant stream of fixed cash flows with no end period.

so, simply put , perpetuity is an annuity with no ending period.

comming to the mathematical expression of perpetuity , it is basically the division of cashflows with some discount rate. it is expressed as follows .(note that cashflows are discounted over indefinite period of time.)

W= + +ਆ =, where: PV = present value C = cash flow 7 = discount rate