Present Value of Annuity

Present Value of Annuity Calculator

 

Present Value of Annuity Formula

Present Value of Annuity = A/i * [1 - (1/(1 + i)ⁿ)]

1.PV = the value at time zero
2.A = Individual Payment in each period
3.i = the discount rate (or interest rate)
4.n = the number of periods

 

What is PV of Annuity?

Present Value (PV) of annuity is used in finance to determine the value of future payments that are paid over a period of time. It takes into consideration the time value of money, a popular concept in economics; a dollar today is worth more than a dollar tomorrow.

 

Present Value of Annuity Example

Greg owns a hotdog stand and he'd like to sell it for $4000. Bob offers him 4 annual payments of $1000 beginning at the end of this first year. What is this proposition, in today's dollars, currently worth if interest is at 6%?

This offer is presently worth: $3465.11

Note that Bob offers $4000, but do not confuse his offer with what it is presently worth (its present value) given the time value of money.

 

An additional example, consider the following:

As a newly retired veteran, Mr. Moto, has been contributing to his retirement account for the past 20 years and he can now begin to withdraw funds from his retirement account. The holder of his retirement account has offered Mr. Moto a lump sum payment of $400,000, or he can accept $28,000 a year for the next 30 years. Mr. Moto wants to see what the value of accepting the $28,000 per year is worth today, to help decide which is the best alternative.

 

Based on the calculation, assuming 6%, the present value of the annuity payments is worth $385,415. Mr. Moto should take the lump sum of $400,000 since it is worth more than the annual payments and he should invest the money. As a side note, 6% is a conservative estimate of how much could be made if invested in the market.