Present Value Calculator
What is a future sum worth in today's money? Discount a lump sum, value an annuity stream, or compare how different rates change PV. Works in any currency.
Try an example
How to Use This Calculator
Tab "Discount to Today"
Enter a future value, an annual discount rate, and the number of years until you receive the money. The calculator shows what that future amount is worth in today's dollars — accounting for the fact that money available now is more valuable than the same amount later.
Tab "Annuity PV"
Enter a regular payment amount, an annual rate, and the total number of periods. Choose whether payments arrive at the end of each period (ordinary annuity — most loans and mortgages) or at the start (annuity due — rent, leases). The calculator shows the total present value of the payment stream. Switch between monthly and annual frequency to match your scenario.
Tab "Compare Discount Rates"
Enter a future value and years ahead — the calculator automatically discounts the same amount at 3%, 5%, 8%, and 10%, showing a sensitivity table. This is one of the most powerful ways to understand how dramatically the choice of discount rate changes valuation.
The Formulas
PV = FV ÷ (1 + r)^n
where FV = future value, r = discount rate per period (decimal), n = number of periods
Present Value of an Ordinary Annuity:
PV = PMT × [(1 − (1 + r)^−n) ÷ r]
where PMT = payment per period, r = rate per period, n = total periods
Present Value of an Annuity Due:
PV = PMT × [(1 − (1 + r)^−n) ÷ r] × (1 + r)
(same as ordinary annuity, multiplied by one extra period)
For monthly payments: divide the annual rate by 12 to get r per period.
These formulas are the foundation of discounted cash flow (DCF) analysis, bond pricing, and retirement planning used by every financial institution worldwide.
Worked Examples
Example 1 — Lump Sum: $100,000 in 10 years at 5%
You are promised $100,000 in 10 years. Your required rate of return (opportunity cost) is 5% per year. What is it worth today?
The promise of $100,000 in 10 years is only worth $61,391 today at a 5% discount rate. The $38,609 difference is the "time discount" — the cost of waiting.
Example 2 — Annuity: $1,000/month for 20 years at 6%
You will receive $1,000 every month for 20 years (240 payments). The annual discount rate is 6%. What is the entire stream worth today?
Despite receiving $240,000 in total, the present value is only $139,581 — because the later payments are worth much less in today's money. The time discount accounts for $100,419 of the difference.
Example 3 — Sensitivity: $50,000 in 5 years across discount rates
The same $50,000 future payment looks very different depending on the discount rate used:
The spread between 3% and 10% is $12,084 — nearly a quarter of the future value. This is why the choice of discount rate is so consequential in investment analysis and business valuation.
Understanding Present Value
Present value is built on a single insight: money today is worth more than the same money tomorrow. This is the time value of money — arguably the most important principle in all of finance. There are three reasons why this is true:
- Investment opportunity. Money available now can be invested immediately to earn a return. A dollar today can become $1.05 in a year at a 5% return.
- Inflation. Over time, prices rise and purchasing power falls. $1,000 today buys more than $1,000 in 10 years.
- Risk. A promised future payment might not materialise. Receiving cash today is certain; a future promise is not.
The discount rate in the PV formula captures all three factors: it represents your minimum required return, which should be high enough to compensate for foregone investment opportunities, inflation, and risk.
Choosing a Discount Rate
The discount rate is the most judgement-intensive input in any present value calculation. Common choices include:
- Risk-free rate — government bond yield (e.g. 4–5% in 2024/25). Used when the future cash flow is guaranteed.
- Opportunity cost — the return you could earn on an alternative investment of similar risk. If you expect your portfolio to return 7%, use 7% to value a competing opportunity.
- Weighted average cost of capital (WACC) — used in corporate finance to discount business cash flows.
- Inflation rate — if you only want to adjust for purchasing power loss, use a pure inflation rate (typically 2–3%).
There is no single "correct" discount rate — it depends on the risk of the cash flow and your personal required return. The Compare tab lets you explore the sensitivity to different rate assumptions.
Ordinary Annuity vs Annuity Due
The timing of payments matters in annuity valuation. An ordinary annuity (also called annuity in arrears) has payments at the end of each period — this is the standard for mortgage payments, car loans, and most debt instruments. An annuity due has payments at the start of each period — the norm for rent, leases, and insurance premiums. Because annuity due payments arrive earlier, they are each worth slightly more in present value terms. The difference is exactly one period of compound interest: PV due = PV ordinary × (1 + r).
Applications of Present Value
Present value analysis is used across virtually every financial decision:
- Bond pricing. A bond's fair price is the present value of its coupon payments plus the face value at maturity, discounted at the current market yield.
- Pension and annuity valuation. The lump-sum equivalent of a pension is calculated as the present value of all projected monthly payments.
- Business valuation (DCF). The intrinsic value of a business is the present value of its future free cash flows, discounted at the WACC.
- Lease vs buy decisions. Comparing the present value of lease payments against the purchase price helps determine the more economical choice.
- Retirement planning. To retire on $5,000 per month for 30 years, you need to accumulate the present value of that annuity stream.
- Legal settlements. Courts and insurers use present value to convert structured settlement streams into lump-sum equivalents.
Key Formulas at a Glance
| Formula | Use | Variables |
|---|---|---|
| PV = FV ÷ (1 + r)^n | Single future payment | FV = future value, r = rate/period, n = periods |
| PV = PMT × [(1 − (1+r)^−n) / r] | Ordinary annuity | PMT = payment/period, r = rate/period, n = periods |
| PV = PMT × [(1 − (1+r)^−n) / r] × (1+r) | Annuity due | Same as above, times one extra period factor |
| r monthly = r annual ÷ 12 | Monthly rate conversion | Use when payments are monthly |