Present Value Calculator

About Present Value Calculator

The Present Value Formula

For a lump sum:

PV = FV / (1 + r)^n

Where FV is the future value, r is the discount rate per period, and n is the number of periods.

For an annuity (equal periodic payments):

PV = PMT x [(1 - (1 + r)^-n) / r]

Where PMT is the payment amount per period.

Worked example (lump sum): Someone promises to pay you $50,000 in 10 years. If you can earn 7% per year on investments, what is that promise worth today?

• PV = $50,000 / (1.07)^10
• PV = $50,000 / 1.9672
• PV = $25,417

The $50,000 in 10 years is worth $25,417 today because if you invested $25,417 at 7%, it would grow to $50,000 by then.

Worked example (annuity): A pension pays $2,000/month for 20 years. At a 5% annual discount rate (0.417% monthly), what is the total stream worth today?

• PV = $2,000 x [(1 - (1.00417)^-240) / 0.00417]
• PV = $2,000 x 151.525
• PV = $303,050

The 240 payments of $2,000 ($480,000 total) have a present value of $303,050. The $176,950 difference is the time value of money - payments received later are worth less than payments received sooner.

How the Discount Rate Affects Present Value

A higher discount rate reduces the present value because it reflects a higher opportunity cost or risk. The impact grows dramatically over longer periods:

Future Value	Years	PV at 3%	PV at 5%	PV at 7%	PV at 10%
$100,000	5	$86,261	$78,353	$71,299	$62,092
$100,000	10	$74,409	$61,391	$50,835	$38,554
$100,000	20	$55,368	$37,689	$25,842	$14,864
$100,000	30	$41,199	$23,138	$13,137	$5,731

At 10% over 30 years, $100,000 in the future is worth only $5,731 today. This explains why distant cash flows are nearly worthless in high-return environments and why pension buyout calculations are so sensitive to the assumed discount rate.

What Discount Rate Should You Use?

Situation	Suggested Rate	Reasoning
Inflation adjustment	2-3%	Central bank inflation target
Risk-free comparison	4-5%	Government bond yield
General investment	7-8%	Long-term stock market average return
Business capital budgeting	8-12%	Weighted average cost of capital (WACC)
Venture capital	20-30%	High risk, high required return

The discount rate should match the risk of the cash flow you are evaluating. A guaranteed government payment deserves a low rate. A speculative business projection deserves a high rate.

Real-World Applications of Present Value

Lottery winnings: A $1 million lottery prize paid as $50,000/year for 20 years is not worth $1 million today. At 5%, the present value is about $623,000. This is why lotteries offer a discounted lump sum option (typically 50-60% of the headline amount).

Pension valuation: A defined benefit pension paying £15,000/year for 25 years at a 4% discount rate has a present value of about £234,000. This is what a transfer value offer would roughly equal.

Legal settlements: Courts use present value to determine lump-sum awards for future lost earnings. A 35-year-old earning $80,000/year with 30 years of lost earnings at a 3% discount rate has a present value claim of about $1.57 million (not $2.4 million nominal).

Capital budgeting: A business evaluating a machine that generates $20,000/year for 8 years at a 10% required return finds the PV is $106,699. If the machine costs $95,000, the Net Present Value (NPV) is positive ($11,699), meaning it is a worthwhile investment.

Present Value vs Future Value

	Present Value	Future Value
Question answered	What is a future amount worth today?	What will today's amount be worth later?
Direction	Discounts backward	Compounds forward
Formula	PV = FV / (1+r)^n	FV = PV x (1+r)^n
Rate is called	Discount rate	Growth rate / interest rate
Used for	Valuing promises, comparing options	Projecting savings and investments

The Discount Factor Table

The discount factor is the multiplier that converts a future amount to present value. It equals 1 / (1 + r)^n. Some commonly referenced discount factors:

Years	3%	5%	7%	10%
1	0.9709	0.9524	0.9346	0.9091
3	0.9151	0.8638	0.8163	0.7513
5	0.8626	0.7835	0.7130	0.6209
10	0.7441	0.6139	0.5084	0.3855
20	0.5537	0.3769	0.2584	0.1486

To use: multiply the future amount by the discount factor. A $10,000 payment in 10 years at 7% is worth $10,000 x 0.5084 = $5,084 today.

For the reverse calculation (what today's money grows to), the future value calculator projects growth with compound interest. To see how inflation specifically erodes purchasing power, the inflation calculator uses the same discounting concept with inflation rates.

Current Benchmark Discount Rates (April 2026)

The "right" discount rate depends on what alternative investment you are giving up. Here are reference points that match the current rate environment, so the PV you calculate reflects real-world opportunities rather than textbook round numbers.

Benchmark	Rate (April 2026)	Source
US 10-year Treasury yield	4.31%	US Treasury, 10 Apr 2026
UK 10-year gilt yield	4.84%	UK DMO, 16 Apr 2026
S&P 500 long-run nominal return	10.3%	Macrotrends, 100-year average
Average S&P 500 WACC	8-10%	NYU Stern (Damodaran), Jan 2026
UK CPI inflation target	2%	Bank of England mandate
US Fed inflation target	2%	Federal Reserve FOMC

For a risk-free calculation (e.g. pricing a government-backed promise), use the 10-year gilt or Treasury yield. For comparing an opportunity to the stock market, the long-run S&P 500 return of roughly 10.3% is the conventional benchmark. For evaluating a company's internal project, the weighted average cost of capital (WACC) of 8-10% is standard for large US firms per NYU Stern's January 2026 dataset.

Nominal vs Real Present Value

Use a real (inflation-adjusted) discount rate when the future cash flow is in today's purchasing power, and a nominal rate when the future cash flow is already stated in future dollars. Mixing the two is a common mistake that can throw PV off by 20% or more over long horizons.

Worked example: A pension pays a nominal £15,000/year for 25 years. If inflation averages 3% and you want the PV in today's purchasing power, first convert the nominal payment to real terms. Year 1 is £15,000 in today's money, but year 25 is only £15,000 / 1.03^24 = £7,391. A cleaner approach is to use the Fisher equation: real rate = (1 + nominal) / (1 + inflation) - 1. If the nominal discount rate is 5%, the real rate is about 1.94%. Discounting £15,000/year for 25 years at 1.94% gives a real PV of roughly £294,000, compared to a naive £211,000 at the nominal rate.

For annuities that are indexed to inflation (like UK state pensions uprated by CPI), this distinction disappears - use the real rate throughout. The Office for National Statistics reports UK CPI averaged 2.8% in 2025 and the Bank of England targets 2% over the medium term, per its Monetary Policy Committee mandate.

Common Mistakes That Distort PV

Small input errors produce large PV errors because of compounding. These are the mistakes we see most often:

• Mixing annual and monthly rates: A 6% annual rate is not the same as 0.5% monthly compounded. Use the monthly rate (r/12) with the monthly count (n x 12), or the annual rate with annual count. Never mix them.
• Using growth rate when risk demands a higher rate: Discounting a risky startup cash flow at 5% produces a falsely high PV. Venture capital typically uses 20-30% to reflect failure risk, per the British Venture Capital Association.
• Ignoring the first payment convention: An annuity due (payments at the start of each period) is worth slightly more than an ordinary annuity (payments at the end). For 20 years at 5%, annuity due PV is 5% higher. This calculator uses the ordinary annuity convention.
• Forgetting that inflation already discounts: If your cash flow grows with inflation, do not also discount for inflation on top of the nominal rate. That double-counts and suppresses the PV.
• Treating the discount rate as certain: PV is highly sensitive to rate choice. At 20 years, moving the rate from 5% to 7% cuts PV by 32%. Always run a sensitivity check with a range of rates before committing to a decision.

PV in Net Present Value (NPV) Analysis

Net Present Value extends the PV concept to multiple future cash flows. NPV = (sum of all future cash flow PVs) - initial investment. A positive NPV means the investment beats the chosen discount rate; a negative NPV means it falls short.

Worked example: A business invests £100,000 today in equipment that generates £30,000/year for 5 years, with a salvage value of £10,000 at the end. At a 10% required return:

• Year 1: £30,000 / 1.10 = £27,273
• Year 2: £30,000 / 1.10^2 = £24,793
• Year 3: £30,000 / 1.10^3 = £22,539
• Year 4: £30,000 / 1.10^4 = £20,490
• Year 5: £40,000 / 1.10^5 = £24,837 (last cash flow plus salvage)
• Total PV of cash flows: £119,932
• NPV = £119,932 - £100,000 = £19,932 (positive, so the investment adds value)

For a full multi-year scenario with irregular cash flows, the investment return calculator handles variable contributions and period-by-period growth.

Sources

• US Treasury - Daily Yield Curve Rates
• FRED - UK 10-Year Gilt Yield
• Macrotrends - S&P 500 Historical Annual Returns
• NYU Stern (Damodaran) - Cost of Capital by Sector
• Bank of England - Inflation and the 2% Target
• Federal Reserve - Statement on Longer-Run Goals
• Investopedia - Present Value

All calculations run in your browser. No data is transmitted.