Present Value Calculator

About Present Value Calculator

Calculate the present value of a future lump sum or a stream of equal payments (annuity). Enter the future amount, discount rate, and number of periods to find what that money is worth today. This is the foundation of the time value of money - the principle that a pound today is worth more than a pound tomorrow.

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.

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