Present Value of Annuity Calculator
Calculate the present value of periodic annuity payments with our free PV of annuity calculator. Switch between ordinary annuity, annuity due, and growing annuity modes. Instant pie charts, payment schedule tables, and step-by-step breakdowns included.
What Is the Present Value of an Annuity?
The present value of an annuity (PVA) is the current lump-sum equivalent of a series of equal future payments, discounted at a specified rate of return. It answers a fundamental question: "How much would I need to invest today to generate this exact stream of payments?"
This concept is central to many financial decisions:
- Pension buyouts — Comparing a lump-sum payout versus monthly pension payments.
- Lottery winnings — Determining the cash value of an annuity prize.
- Loan pricing — The loan amount equals the PV of all future repayments.
- Lease valuation — Calculating the fair value of a series of lease payments.
- Insurance settlements — Converting structured payouts into a single present value.
How to Calculate PV of an Annuity
The present value of an annuity depends on three key variables: the payment amount (PMT), the discount rate per period (r), and the total number of periods (n). The core formula discounts each individual payment back to the present and sums them.
Ordinary Annuity (End-of-Period Payments)
Annuity Due (Beginning-of-Period Payments)
Where:
- PMT = Payment amount per period
- r = Discount rate per period (annual rate ÷ compounding frequency)
- n = Total number of payment periods
Step-by-Step Calculation
Suppose you receive $5,000 per year for 10 years at a 7% annual discount rate:
PV = $5,000 × [(1 − 0.5083) / 0.07]
PV = $5,000 × 7.0236 = $35,118.08
Total payments received: $50,000. Present value: $35,118 — meaning you save $14,882 in time-value discount.
Ordinary Annuity vs. Annuity Due — PV Differences
The timing of payments significantly impacts the present value:
| Feature | Ordinary Annuity | Annuity Due |
|---|---|---|
| Payment timing | End of each period | Beginning of each period |
| Common examples | Mortgage payments, bond coupons | Rent, insurance premiums, leases |
| PV relationship | PVordinary | PVdue = PVordinary × (1 + r) |
| Higher PV? | Lower | Always higher by factor (1 + r) |
Ordinary PV = $20,756.07 | Annuity Due PV = $21,793.87
The annuity due is $1,037.80 higher because each payment is one period closer to today.
Present Value of Growing Annuity
A growing annuity is a series of payments that increase at a constant rate g each period. This is commonly used to value pensions with cost-of-living adjustments, salaries with annual raises, or revenues that grow with inflation.
This formula is valid when the discount rate r is not equal to the growth rate g. When r = g:
Growing Annuity Example
A pension pays $30,000 in Year 1 and grows at 2% per year for 25 years. Discount rate: 6%.
PV = $30,000 × [(1 − 0.3751) / 0.04]
PV = $30,000 × 15.6226 = $468,678
Without growth (fixed $30,000/year), the PV would be $383,442 — the 2% annual increase adds $85,236 in present value.
PV of Annuity Formula in Excel
Microsoft Excel and Google Sheets include a built-in =PV() function that calculates annuity present values directly:
- rate — Discount rate per period (e.g., 6%/12 for monthly)
- nper — Total number of periods
- pmt — Payment per period (enter as negative for income received)
- fv — Future value (optional, usually 0 for annuity PV)
- type — 0 = end of period (ordinary), 1 = beginning (due)
Excel Examples
=PV(0.05, 20, -1000) → $12,462.21
=PV(0.05, 20, -1000, 0, 1) → $13,085.32
=PV(0.06/12, 120, -500) → $44,955.04
Frequently Asked Questions
-
The present value of an annuity is the current lump-sum equivalent of a series of equal future payments, discounted at a given interest rate. It represents how much money you would need to invest today to replicate the exact same stream of future payments. For example, $1,000/year for 20 years at 6% has a PV of $11,469.92.
-
For an ordinary annuity (end-of-period payments): PV = PMT × [(1 − (1+r)−n) / r]. For an annuity due (beginning-of-period): multiply by an additional (1 + r). Here PMT is the payment per period, r is the discount rate per period, and n is the total number of periods.
-
An ordinary annuity assumes payments at the end of each period, while an annuity due assumes payments at the beginning. The annuity due PV is always higher by a factor of (1+r) because each payment is discounted for one fewer period, making it worth more in today's dollars.
-
Use
=PV(rate, nper, pmt, [fv], [type]). For example, PV of $1,000 annual payments for 20 years at 5%:=PV(0.05, 20, -1000)returns $12,462.21. Set the last parameter to 1 for annuity due. Note: Excel requires PMT as negative for cash inflows. -
A growing annuity is a series of payments that increase at a constant rate (g) each period. Its PV formula is PV = PMT × [(1 − ((1+g)/(1+r))n) / (r − g)]. This is useful for valuing income streams that grow with inflation, salary increases, or revenue growth. The PV is higher than a flat annuity because later payments are larger.
-
Because of the time value of money. Each future payment is worth less than its face value today since you could invest money now and earn a return. The further a payment is in the future, the more it is discounted. At a 6% rate, $1,000 received 20 years from now is only worth $312 today.
-
The rate should reflect the risk and opportunity cost of the cash flows. Use the risk-free rate (3–5%) for guaranteed payments like Treasury bonds; expected market return (7–10%) for investment comparisons; or your personal required rate of return. Higher risk warrants a higher discount rate.