Present Value Calculator
This present value calculator discounts a future amount or a series of payments back to today: 10,000 due in ten years is worth only 6,755.64 now at 4%. It handles lump sums, regular annuities and perpetuities.
Example: Future amount 10,000 · Term in years 10 · Discount rate per year 4 % · Regular payment (annuity) 0 · Payments per year: monthly → Present value: Present value: 6,755.64. Source: Wikipedia – Present value. Updated: .
How it is calculated
The present value is what a payment due in the future is worth today – calculated with an interest rate called the discount rate. It answers the question: how much would I have to invest now to have exactly this amount later?
The formulas
- Lump sum: present value = amount ÷ (1 + rate)ⁿ. 10,000 in 10 years at 4%: 10,000 ÷ 1.04¹⁰ = 6,755.64.
- Annuity (payments at period end): PV = payment · (1 − (1 + i)^−N) ÷ i, with the periodic rate i and N payments. 1,000 per year for 10 years at 5% is worth 7,721.73 today.
- Annuity due (payments at period start): the annuity value is multiplied by (1 + i), because every payment arrives one period earlier.
- Perpetuity: PV = payment ÷ i. With 1,000 per year at 5% that gives 20,000.
Which rate to use?
The discount rate reflects what you could otherwise earn on the money, plus a premium for risk. The higher it is, the smaller the present value, so the table also shows values at rates above and below yours. For payments several times a year, the effective annual rate is converted into an equivalent periodic rate.
The opposite direction – what money today is worth later – is covered by the future value calculator. Several uneven cash flows are valued by the IRR calculator including net present value, and the withdrawal calculator shows how long capital lasts under regular withdrawals.
Frequently asked questions
How do you calculate present value?
Divide the future amount by (1 + rate) raised to the number of years. 5,000 in 3 years at 3% has a present value of 5,000 ÷ 1.03³ = 4,575.71.
What is the present value of an annuity?
It is the sum of all future payments, each discounted individually to today. It tells you which lump sum the annuity is worth now, for example when comparing a buyout offer.
What is the difference between ordinary annuity and annuity due?
An ordinary annuity pays at the end of each period, an annuity due at the start. Payments at the start arrive one period earlier and therefore have a higher present value.
Why does the present value fall when the rate rises?
Because at a high rate less money today is enough to reach the same amount later. The discount factor gets smaller.
What is a perpetuity?
A payment stream that never ends. Its present value is the payment divided by the rate – but only for a rate above 0%.
Sources and legal basis
As of: · Editorial policy
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