A Perpetuity a type of annuity with payments that last forever.

Perpetuity Immediate:

This is a perpetuity with payments at the end of the interest crediting period.

Perpetuity Immediate PV Proof

Recall the interest discounting formula v where:

v =

1

1 + i

The payments continue forever Write the present value of a payment of 1 each period with notation a_{∞|i} with interest rate (i) as follows a_{∞|i} = v + v^{2} + v^{3} + · · ·

a_{∞|i} =

v

1 - v

Since 1 - v = iv, we have

a_{∞|i} =

v

iv

Cancel the v on the top and bottom:

a_{∞|i} =

v

iv

a_{∞|i} =

1

i

Plug in a payment of P each period:

a_{∞|i} =

P

i

Perpetuity Due:

This is a perpetuity with payments at the beginning of the interest crediting period.

Perpetuity Due PV Formula Proof

Recall the interest discounting formula d = iv where: The payments continue forever Write the present value of a payment of 1 each period with notation ä_{∞|i} with interest rate (i) as follows a_{∞|i} = 1 + v + v^{2} + · · ·

ä_{∞|i} =

1

1 - v

Since d = 1 - v, we have

ä_{∞|i} =

1

d

Since d = i/(1 + i), we take the reciprocal of this since it's in the denominator and we have

Free Perpetuity Calculator - Walks you through the definition of a perpetuity, the present value of a perpetuity immediate, and the present value of a perpetuity due.

What 2 formulas are used for the Perpetuity Calculator?

What 4 concepts are covered in the Perpetuity Calculator?

discount rate

the interest rate used in discounted cash flow (DCF) analysis to determine the present value of future cash flows. Key Takeaways.

interest rate

the proportion of a loan that is charged as interest to the borrower or proportion of principal credit given to a depositor

perpetuity

An infinite stream of payments

present value

the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest. PV = FV/(1 + i)^{n} where I is the interest rate per period, PV = Present Value, and FV = Future Value