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
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%? Present Value of Annuity (back to top of page)
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.
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.
Present Value of Annuity (back to top of page)