Present Value Calculator
Discount a single future amount, or a stream of equal payments at the end or start of each period, back to today's dollars.
Present Value
$59,777.15
Total Future Amount
$120,000.00
Discount (Future − Present)
$60,222.85
Rate per Period
0.6667%
Number of Periods
240
How it works
A dollar you receive later is worth less than a dollar today, because today's dollar could be invested in the meantime. Present value answers the reverse question: how much would you need to invest today, at your discount rate, to end up with the future amount?
For a single amount the calculator divides it by one plus the rate per period, raised to the number of periods. For a series of equal payments it discounts every payment back to today and adds them up. Payments at the start of each period (an annuity due) are each discounted one period less, so they are worth more today than the same payments at the end of each period.
The discount rate is the most important input and it is your choice: the return you could earn on a comparable investment, an interest rate you are offered, or a rate set by an agreement. A higher rate gives a lower present value.
Formula
r = annual rate ÷ periods per year n = years × periods per year single amount: PV = FV ÷ (1 + r)^n ordinary annuity: PV = PMT × (1 − (1 + r)^−n) ÷ r (PMT × n when r = 0) annuity due: PV = PMT + ordinary annuity PV over n − 1 periods (= ordinary PV × (1 + r))
Example
Payments of $500 at the end of every month for 20 years, discounted at 8% a year compounded monthly, have a present value of $59,777.15. That matches the example in Microsoft's documentation for Excel's PV function. The payments total $120,000, so $60,222.85 of their face value is the cost of waiting.
If the same payments arrive at the start of each month instead, the present value rises to $60,175.66. A single $10,000 received in 10 years, discounted at 6% compounded annually, is worth $5,583.95 today.
Assumptions and limitations
- The discount rate is an assumption you enter and is held constant for the whole period. Real rates change.
- For a series, payments are equal, made once per compounding period, and the payment frequency matches the compounding frequency.
- Taxes, fees and inflation are not modelled unless you build them into the rate (use a real, after-inflation rate to get today's purchasing power).
- Results are estimates for planning and are for informational and educational purposes only. They are not financial, tax or legal advice.
Frequently asked questions
What discount rate should I use?
People often use the return they could reasonably expect from an alternative with similar risk. To value a pension or settlement offer, a high-quality bond yield is a common choice; to compare with paying off debt, people often use that debt's interest rate. Trying a few rates shows how sensitive the answer is.
Why is an annuity due worth more than an ordinary annuity?
Each payment arrives one period sooner, so it is discounted one period less. The whole present value is exactly one period's growth, (1 + r), higher.
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