Present Value of Annuity Calculator
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The Present Value of Annuity Calculator helps investors, financial planners, and corporate analysts calculate today’s lump-sum cash worth (Present Value) of a series of equal future recurring cash payments. Evaluate both Ordinary Annuities (end-of-period payments) and Annuities Due (beginning-of-period payments).
The Present Value of Annuity Formulas
The present value of an ordinary annuity (PVA) discounts equal recurring payments (PMT) at a fixed interest discount rate (r) over n periods:
Ordinary Annuity PVA = PMT × [ 1 - (1 + r)^-n ] / r
Annuity Due PVA = PMT × [ 1 - (1 + r)^-n ] / r × (1 + r)
Where:
- PMT: Equal recurring dollar cash flow payment per period.
- r: Discount interest rate per period (Annual interest rate divided by payment frequency).
- n: Total number of recurring payment periods.
Present Value of Annuity Valuation Benchmarks
Compare present lump-sum values for receiving $1,000 per month ($12,000/year) across discount rates and payment durations (Ordinary Annuity):
| Payment Duration | Total Nominal Cash Paid | PVA @ 5.00% Discount | PVA @ 7.00% Discount | PVA @ 9.00% Discount |
|---|---|---|---|---|
| 5 Years (60 mos) | $60,000 | $52,990.71 | $50,502.00 | $48,173.37 |
| 10 Years (120 mos) | $120,000 | $94,281.35 | $86,126.35 | $78,941.69 |
| 20 Years (240 mos) | $240,000 | $151,525.31 | $129,033.57 | $111,144.95 |
Step-by-Step Present Value Calculation Example
Here is an example calculating the Present Value of receiving $5,000 per year for 10 years at a 6.00% discount rate (Ordinary Annuity):
- Identify Inputs: Payment PMT = $5,000, Discount Rate r = 6.00% (0.06), Term n = 10 years.
- Calculate Discount Factor:
(1 + 0.06)^-10 = 0.558395. - Calculate Term Factor:
[ 1 - 0.558395 ] / 0.06 = 0.441605 / 0.06 = 7.360087. - Multiply by Annual Payment:
$5,000 × 7.360087 = $36,800.44. - Result: Receiving $5,000 annually for 10 years is worth $36,800.44 in today’s cash value.
Frequently Asked Questions
Why is the Present Value of an annuity lower than total cash received?
Due to the time value of money, receiving money today is worth more than receiving the same amount in the future because today’s money can be invested to earn interest.
How is Present Value of Annuity used for lottery payouts?
Lottery organizations calculate the Present Value of an annuity to determine the immediate lump-sum cash option payout versus taking 30 annual annuity payments.
What is the difference in Present Value between Ordinary Annuity and Annuity Due?
An Annuity Due has a higher present value than an Ordinary Annuity because payments arrive one period earlier, incurring less interest discounting.
How does discount rate affect Present Value?
A higher discount rate lowers the present value of future cash flows, while a lower discount rate increases the present value of future payments.