Loading calculator...
Present Value of Annuity Calculator
Calculate the present value of a series of future payments. Compare lump sum vs annuity offers, value pensions, and analyze leases.
Formula:PV = PMT × [1 - (1+r)^(-n)] / r
Present Value
$12,462
Worth today of 20 payments of $1,000 at 5% discount rate
Breakdown
Total Payments
Nominal value
$20,000
Present Value
Today's worth
$12,462
Interest/Discount
Time value of money
$7,538
Key Metrics
PV Factor12.4622
Effective Annual Rate5.00%
Payment/Value Ratio160.5%
Quick Scenarios
Annuity Details
Enter your payment parameters
$
Amount received each period
%
Interest/discount rate
Total number of payments
12 for monthly, 4 for quarterly, etc.
How often interest compounds
When payments are received
Present Value
$12,462
Today's worth
Total Payments
$20,000
20 payments
Interest/Discount
$7,538
Time value of money
PV Factor
12.4622
Per $1 payment
Discounted Cash Flow Diagram
Compare nominal payments vs. their present values over 20 periods
How to read this chart: The gray area shows nominal payment amounts, while the blue area shows their present values. Notice how later payments have significantly lower present values due to discounting.
Cumulative Present Value
How present value accumulates as payments are received
Final Present Value: $12,462
PV Breakdown
Present value vs. interest/discount portion
Present Value
$12,462
62.3% of total
Interest/Discount
$7,538
37.7% of total
Discount Factor Over Time
How much $1 in each future period is worth today
The discount factor shows the present value of $1 received in each future period. A factor of 0.50 means $1 in that period is worth $0.50 today.
Period-by-Period Breakdown
| Period | Payment | Discount Factor | Present Value | Cumulative PV |
|---|---|---|---|---|
| 1 | $1,000 | 95.24% | $952 | $952 |
| 2 | $1,000 | 90.70% | $907 | $1,859 |
| 3 | $1,000 | 86.38% | $864 | $2,723 |
| 4 | $1,000 | 82.27% | $823 | $3,546 |
| 5 | $1,000 | 78.35% | $784 | $4,329 |
| 6 | $1,000 | 74.62% | $746 | $5,076 |
| 7 | $1,000 | 71.07% | $711 | $5,786 |
| 8 | $1,000 | 67.68% | $677 | $6,463 |
| 9 | $1,000 | 64.46% | $645 | $7,108 |
| 10 | $1,000 | 61.39% | $614 | $7,722 |
| 11 | $1,000 | 58.47% | $585 | $8,306 |
| 12 | $1,000 | 55.68% | $557 | $8,863 |
| 13 | $1,000 | 53.03% | $530 | $9,394 |
| 14 | $1,000 | 50.51% | $505 | $9,899 |
| 15 | $1,000 | 48.10% | $481 | $10,380 |
| 16 | $1,000 | 45.81% | $458 | $10,838 |
| 17 | $1,000 | 43.63% | $436 | $11,274 |
| 18 | $1,000 | 41.55% | $416 | $11,690 |
| 19 | $1,000 | 39.57% | $396 | $12,085 |
| 20 | $1,000 | 37.69% | $377 | $12,462 |
Formulas Used
Ordinary Annuity (End of Period)
PV = PMT x [1 - (1+i)^-n] / iAnnuity Due (Beginning of Period)
PV = PMT x [1 - (1+i)^-n] / i x (1+i)Present Value
$12,462
Worth today of 20 payments of $1,000 at 5% discount rate
Breakdown
Total Payments
Nominal value
$20,000
Present Value
Today's worth
$12,462
Interest/Discount
Time value of money
$7,538
Key Metrics
PV Factor12.4622
Effective Annual Rate5.00%
Payment/Value Ratio160.5%
Quick Answer: What is the Present Value of an Annuity?
The present value of an annuity is the current worth of a series of future payments, discounted at a given interest rate. For ordinary annuities: PV = PMT x [1 - (1+i)^-n] / i. Example: $1,000/month for 20 years at 5% has a present value of approximately $151,525. This tells you how much a lump sum today would be equivalent to receiving those future payments.
Key Facts
- Present value answers: "What is a stream of future payments worth today?"
- Higher discount rates result in lower present values
- Annuity due (beginning of period) has ~3-5% higher PV than ordinary annuity
- Deferred annuities are worth less because you wait longer for payments
- Perpetuity PV = Payment / Rate (for constant payments)
- Gordon Growth Model: PV = PMT / (r - g) for growing perpetuities
- PV Factor tells you the present value per $1 of payment
Adjust Discount Rate
See how discount rate affects the present value of your annuity
1%5%15%
Personalized Insights
3 insights based on your inputs
Note
At 5% discount rate, $20,000 in future payments is worth $12,462 today—a 37.7% discount for time value.
Note
If payments came at period beginning (annuity due) instead of end, the present value would be $52 higher.
Note
PV factor of 12.4622 means each $1 of payment is worth $12.4622 today. Use this to quickly value any payment stream.
Related Calculators
Explore other tools that might help
Frequently Asked Questions
The present value of an annuity is the total current worth of all future payments, taking into account the time value of money. It answers: "How much money would I need today to generate this stream of future payments?" This is crucial for comparing lump-sum offers to periodic payments.
Calculate the present value of the annuity using an appropriate discount rate (your expected investment return). If the lump sum offered is greater than the PV, take the lump sum. If it's less, the annuity is more valuable. Also consider factors like investment skill, risk tolerance, and liquidity needs.
Use a rate that reflects your opportunity cost - what return you could earn investing the money elsewhere. Common choices: risk-free rate (Treasury bonds, 4-5%), conservative portfolio (5-6%), moderate portfolio (7-8%). For company valuations, use the weighted average cost of capital (WACC).
A deferred annuity is one where payments don't start immediately but begin after a waiting period. For example, a retirement annuity purchased at age 55 that starts paying at age 65 has a 10-year deferral. The present value is lower because payments are further in the future.
A perpetuity is an annuity that pays forever. While uncommon, examples include certain preferred stocks and endowment funds. The present value is simply PV = PMT / r. For a growing perpetuity (Gordon Growth Model), PV = PMT / (r - g) where r must be greater than g.
Annuity due (payments at beginning of period) has a higher present value than ordinary annuity (payments at end) because each payment is received sooner, requiring less discounting. The difference is approximately (1 + i) or about 3-8% depending on the interest rate.
The Present Value Factor (or annuity factor) tells you the present value per $1 of periodic payment. PV Factor = [1 - (1+i)^-n] / i. To find the present value of any annuity, multiply the payment by this factor. It's useful for quick calculations and comparisons.
To value a pension: 1) Estimate monthly payment amount, 2) Estimate number of payments (life expectancy minus retirement age, times 12), 3) Choose a discount rate (typically 4-6%), 4) Calculate present value. Don't forget to consider COLA adjustments (use growing annuity formula).
Joseph OrdunaFounder & Software Engineer
Full-stack software engineer specializing in embedded systems, web architecture, and AI/ML. Founder of Practical Web Tools. Built the gesture-controlled drone IP acquired by KD Interactive (Aura Drone, sold on Amazon).
Present Value
$12,462
Worth today of 20 payments of $1,000 at 5% discount rate
Breakdown
Total Payments
Nominal value
$20,000
Present Value
Today's worth
$12,462
Interest/Discount
Time value of money
$7,538
Key Metrics
PV Factor12.4622
Effective Annual Rate5.00%
Payment/Value Ratio160.5%