Present Value Calculator
What a future lump sum and a stream of payments are worth today at a given discount rate — with the discount factor, the annuity value and a period-by-period table.
Present Value Calculator: with the default inputs, present value is $13,860.87.
A single amount received at the end of the term. Use 0 if there isn't one.
A level cash flow received every period — the annuity part. Use 0 for a lump sum only.
The return you could earn elsewhere on money of the same risk.
Both the payments and the discounting use this frequency.
What the whole stream is worth in today's dollars.
- PV of the lump sum
- $6,139.13
- PV of the payments
- $7,721.73
- Total nominal cash
- $20,000Every dollar received, undiscounted.
- Value lost to discounting
- $6,139
- Discount factor on the lump sum
- 0.6139131 ÷ (1 + i)^n — the value of $1 received at the end.
- Annuity factor
- 7.721735The present value of $1 per period for the whole term.
- Number of periods
- 10
Assumptions
- One constant discount rate for the whole term, compounded at the payment frequency.
- Payments are level and certain; no default risk or growth is modelled.
- The lump sum arrives at the end of the final period.
- Nominal cash flows discounted at a nominal rate — do not mix real and nominal.
| Period | Cash received | Discount factor | Present value |
|---|---|---|---|
| 1 | $1,000 | 0.952381 | $952.38 |
| 2 | $1,000 | 0.907029 | $907.03 |
| 3 | $1,000 | 0.863838 | $863.84 |
| 4 | $1,000 | 0.822702 | $822.70 |
| 5 | $1,000 | 0.783526 | $783.53 |
| 6 | $1,000 | 0.746215 | $746.22 |
| 7 | $1,000 | 0.710681 | $710.68 |
| 8 | $1,000 | 0.676839 | $676.84 |
| 9 | $1,000 | 0.644609 | $644.61 |
| 10 | $11,000 | 0.613913 | $6,753.05 |
The lump sum is added to the final period.
How this is worked out
The formula
PV = FV ÷ (1 + i)^n + PMT × [ 1 − (1 + i)^−n ] ÷ i (× (1 + i) for an annuity due) FV = lump sum received at the end PMT = level payment each period i = discount rate ÷ periods per year n = periods per year × years At i = 0 the annuity term collapses to PMT × n.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Future lump sum
- A single amount received at the end of the term. Use 0 if there isn't one.in dollars · defaults to 10000
- Payment each period
- A level cash flow received every period — the annuity part. Use 0 for a lump sum only.in dollars · defaults to 1000
- Discount rate
- The return you could earn elsewhere on money of the same risk.a percentage · from 0 to 100 · defaults to 5
- Term
- A number.from 0 to 100 · whole numbers only · defaults to 10
- Periods per year
- Both the payments and the discounting use this frequency.Annually (1) · Semi-annually (2) · Quarterly (4) · Monthly (12)
- Payments arrive(under More options)
- Choose one of 2 options.End of period (ordinary annuity) · Beginning of period (annuity due)
What you get back
- Present valuemain answer
- What the whole stream is worth in today's dollars.
- PV of the lump sum
- PV of the payments
- Total nominal cash
- Every dollar received, undiscounted.
- Value lost to discounting
- Discount factor on the lump sum
- 1 ÷ (1 + i)^n — the value of $1 received at the end.
- Annuity factor
- The present value of $1 per period for the whole term.
- Number of periods
What this assumes
- One constant discount rate for the whole term, compounded at the payment frequency.
- Payments are level and certain; no default risk or growth is modelled.
- The lump sum arrives at the end of the final period.
- Nominal cash flows discounted at a nominal rate — do not mix real and nominal.
About this calculator
A dollar you'll be handed in ten years is not worth a dollar today — you could have invested today's dollar in the meantime. Present value is the size of the cheque you'd accept right now instead of waiting, given the return you could otherwise earn. It is the single most useful idea in finance, and everything from bond pricing to a pension buyout to a lottery payout runs on it.
How to use it
Enter the future lump sum, the payment stream, or both. Set the discount rate to the return you could earn on money of the same risk — for a safe, guaranteed payment that's a Treasury yield; for a business project it's your cost of capital; for a personal decision your borrowing rate is a defensible proxy. Match the periods per year to how the money actually arrives. If the payments land at the start of each period (rent, leases, most pension checks), switch to annuity due under More options; each payment then earns an extra period of discounting relief and the value rises by a factor of (1 + i).
Reading the results
- Present value is the answer: what the whole stream is worth today.
- Discount factor is the value of $1 received at the end. At 5% over 10 years it is 0.613913 — so $1,000 in ten years is worth $613.91 now.
- Annuity factor is the same thing for $1 per period. It is what turns a monthly pension into a lump sum.
- Value lost to discounting is the gap between the nominal cash and its present value. Over long horizons that gap is most of the money.
The lump-sum-versus-payments decision
This is the calculator for "should I take the $500,000 buyout or the $2,800 a month?" Compute the present value of the payment stream at a rate you could actually earn, and compare. Two cautions: the payments may last as long as you do, so the term is a guess about longevity, and the discount rate does the heavy lifting — at 4% the stream might win, at 7% the lump sum. Run it at both ends of a plausible range before deciding anything.
Where it misleads
Present value says nothing about risk beyond whatever you baked into the rate; a promised payment from a shaky payer deserves a higher discount rate, not the same one. Inflation is handled by choosing consistently — discount nominal cash flows at a nominal rate, or real cash flows at a real rate, never a mix. And a stream that is not level (raises, COLA increases, irregular projects) needs the IRR or payback calculators instead, which take a cash flow at a time.
Frequently asked questions
▸What discount rate should I use?
The return you could earn on an alternative of similar risk. For guaranteed cash flows use a Treasury yield of matching maturity; for corporate projects use the weighted average cost of capital; for household decisions your borrowing rate is a reasonable stand-in.
▸How do I compare a lump sum to monthly payments?
Take the present value of the payments at a rate you could realistically earn and compare it to the lump sum. If the PV is higher, the payments are worth more — subject to the payer staying solvent and you living long enough to collect them.
▸What is the difference between an ordinary annuity and an annuity due?
Ordinary annuities pay at the end of each period, annuities due at the beginning. An annuity due is worth (1 + i) times as much, because every payment arrives one period sooner.
▸Should I discount at the inflation rate?
Only if your cash flows are in nominal dollars and you care solely about purchasing power. The cleaner method is to discount nominal cash flows at a nominal rate — one that already includes expected inflation — or express everything in today's dollars and use a real rate.
▸Why does the present value fall so fast at high rates?
Because discounting is exponential. At 5%, $1 in 30 years is worth 23 cents; at 10% it is worth 6 cents. Doubling the rate does far more than halve the value over long horizons.
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