Present Value Calculator

Now, or later?

Someone offers you five lakh, payable in eight years. Or you can have some smaller amount today. How much smaller before you would rather wait?

Almost everyone has an instinct about this and almost nobody can put a number on it. The instinct is right, though. Money in your hand today is worth more than the same money later, because you can do things with it in the meantime. Lend it, invest it, pay off something that was costing you interest, or just get the thing you wanted eight years earlier.

Present value is what you get when you put arithmetic behind that instinct. It takes an amount arriving on some future date and converts it into what it is worth to you now, and once you have that number you can compare two offers that arrive at completely different times.

This calculator wants three things. What the future amount is, the rate you want to discount it at, and how many periods away it sits.

The formula is the easy part

PV = FV / (1 + r)ⁿ

Read it as compound interest running backwards. If money grows by multiplying by (1 + r) every period, then to walk back to today you divide by (1 + r) once for every period you travel.

The calculator takes the rate as a percentage and does the division by 100 for you, and it rounds the answer to two decimal places. Both the rate and the number of periods are capped at 100.

That is all the maths there is on this page. The rest of it is about the one input that decides everything.

Choosing the rate is the hard part

Here is the uncomfortable thing about present value, and it is the reason this section exists at all.

The calculation is exact. The rate you feed it is a judgement call. So the precision of the answer is entirely borrowed from the confidence of your assumption, and it is easy to forget that once you are looking at a number with two decimal places on it.

How much does it matter? Take our five lakh in eight years and run it at four plausible rates.

Same money, same date, and a spread of a lakh and a half between the top and bottom rows. Nothing changed except one assumption.

So what should you actually put in that box? It depends on what you are asking, and there are three defensible answers.

What you would otherwise earn

The most common and most honest choice for personal money. If turning down the future payment means you could take a smaller amount today and put it in a fixed deposit at 7 percent, then 7 percent is your rate. You are asking how much you would need today to end up with the same amount by the same date.

What the money costs you

For a business, the rate is usually the cost of the money being tied up. If a company funds itself with a mix of debt and equity that averages 11 percent, that is the bar, and our WACC calculator works it out. Discounting at less than what your capital costs will make bad projects look acceptable.

What somebody official says

This one surprises people. For certain purposes there is a legally prescribed rate and you do not get to pick.

In the United States, the Internal Revenue Service publishes a rate every month under section 7520 of the tax code, specifically for discounting annuities, life estates and remainder interests to present value. It is set at 120 percent of the applicable federal mid-term rate, compounded annually, then rounded to the nearest two tenths of a percent. If you are valuing a future interest for gift or estate tax, that is the rate, and your opinion about it is not required.

Even if you are nowhere near a US estate return, the existence of that rate is useful. It tells you what a government thinks a defensible medium-term discount rate looks like, and it is published every single month.

A habit worth forming

Run your number twice. Once at the rate you think is right, and once a few points either side of it. If the decision flips between those two runs, you do not have an answer yet, you have an assumption doing all the work. If the decision holds across the range, you can trust it.

And then time does the rest

The rate is the choice. Time is the multiplier on that choice, and it compounds hard.

Hold the rate at 9 percent and move the date instead:

At 9 percent, every eight years roughly halves what a future sum is worth today. That is the rule of 72 running in reverse, and once you notice it you cannot unsee it. A promise of money twenty four years out is worth about an eighth of its face value, which is why very long dated promises are worth so much less than they sound.

It also explains something about the periods box. It says periods, not years, for a reason. If your rate is quarterly then your periods are quarters, and eight years becomes 32. Rate and periods have to describe the same slice of time or the answer is meaningless. Our present value of a lump sum calculator goes into that matching problem properly.

Working one through

Back to the offer we started with. ₹5,00,000, arriving in 8 years, discounted at 9 percent a year.

Nine percent becomes 0.09. One plus that is 1.09. Raise 1.09 to the eighth power and you get 1.99256. Then divide:

5,00,000 divided by 1.99256 = ₹2,50,933.14

So that promise of five lakh in eight years is worth a little over two and a half lakh to you today, if 9 percent is genuinely what your money could otherwise be doing.

Which means the gap between the two is ₹2,49,066.86. That is not a fee anyone charges you. It is what eight years of waiting costs, priced at 9 percent.

The practical reading: if someone offers you anything above ₹2,50,933.14 in cash today instead of the future five lakh, take the cash. Below it, wait. And notice how much that threshold moved in the table further up when the rate changed, because that is the real lesson.

Where this actually gets used

Present value sounds academic until you notice how many ordinary decisions are secretly this calculation.

A settlement offer. An insurer offers a lump sum now instead of a payout later. Discounting the later figure tells you whether the offer is generous or just convenient for them.

A pension choice. Take the commuted lump sum, or the monthly pension. The lump sum is a number you can see. The pension is a stream that has to be discounted before the two are comparable.

Bond pricing. A bond is a set of dated promises, and its fair price is the present value of all of them. Nothing more mysterious than that.

A deposit or maturity value. An endowment policy that pays out in twelve years, a bond maturing in five. Discount it and you find out whether it beats simply putting the money somewhere else.

Anything with a deferred payment. A supplier offering you 90 days credit is offering you a discount, whether or not either of you calls it that.

For streams of payments rather than a single amount, you want the annuity tools instead. Our PVIFA calculator handles equal payments and the discounted cash flow calculator handles uneven ones.

Checking the answer

Present value has a lovely property: it undoes itself. Take the answer, compound it forward at the same rate for the same number of periods, and you should land back on the future value you started with.

So take 2,50,933.14, grow it at 9 percent for 8 years, and you get 5,00,000 back. The US Securities and Exchange Commission publishes a free compound interest calculator that will do that leg for you, which makes it a genuinely independent check rather than us marking our own homework.

Two other quick sanity tests. The present value should always be smaller than the future value as long as the rate is above zero, and it should get smaller as either the rate or the number of periods goes up. If either of those goes the wrong way, something has been typed wrong.

And one small thing worth remembering about what this number is not. It is a nominal figure, so if you want to know what it means in buying power you also need to think about inflation, which our real rate of return calculator handles. It also assumes the future payment definitely arrives. If there is a real chance it does not, the rate has to carry that risk, which is exactly why riskier things get discounted harder.

Questions people ask

What discount rate should I use?

The return you could get on the same money at similar risk. For personal decisions that is often a fixed deposit or index fund rate. For a business it is usually the cost of capital. For US gift and estate valuations the IRS publishes a mandatory rate each month under section 7520.

Is present value the same as net present value?

Not quite. Present value discounts amounts coming in. Net present value discounts everything, then subtracts what you had to put in to get it. NPV is present value with the cost netted off.

Does the periods box mean years?

Only if your rate is annual. The rate and the periods have to match the same length of time. A quarterly rate needs a count of quarters.

Can I use the inflation rate as my discount rate?

You can, and it answers a specific question: what is that future sum worth in today's buying power. That is a different question from what it is worth against what you could earn, so be clear about which one you are asking.

What if I enter a rate of zero?

You get the future value back unchanged, which is correct. A zero discount rate says waiting costs you nothing.

Why does it stop at 100?

Both the rate and the period count are capped at 100. That covers essentially every real discounting problem, and past those values the arithmetic produces numbers too small to be meaningful anyway.

I have several payments on different dates, not one.

Discount each one separately and add the results, or use the discounted cash flow calculator. If the payments are all equal and evenly spaced, the PVIFA calculator does it in one step.

References

A note on where the outside claims here come from. The most surprising one, that a discount rate is sometimes prescribed by law rather than chosen, is the US Internal Revenue Service's section 7520 rate, and both the rate itself and the regulation governing its use are linked below. The compounding relationship that present value reverses is defined by the Securities and Exchange Commission's investor education office, whose free calculator can be used to check any answer from this page by running it forward. The treatment of discounting as the foundation of investment appraisal, and the argument for testing a decision across a range of rates rather than trusting one, follows the standard corporate finance text.

1. Internal Revenue Service, Section 7520 interest rates, the monthly rate prescribed for discounting annuities, life estates and remainder interests to present value, set at 120 percent of the applicable federal mid-term rate compounded annually and rounded to the nearest two tenths of a percent. https://www.irs.gov/businesses/small-businesses-self-employed/section-7520-interest-rates
2. Cornell Law School, Legal Information Institute, 26 CFR § 1.7520-1, Valuation of annuities, unitrust interests, interests for life or terms of years, and remainder or reversionary interests. https://www.law.cornell.edu/cfr/text/26/1.7520-1
3. U.S. Securities and Exchange Commission, Office of Investor Education and Advocacy, Compound Interest, Investor.gov glossary. https://www.investor.gov/introduction-investing/investing-basics/glossary/compound-interest
4. U.S. Securities and Exchange Commission, Compound Interest Calculator, Investor.gov, useful for compounding a present value forward to verify it returns the original future value. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
5. Brealey, R.A., Myers, S.C., and Allen, F., Principles of Corporate Finance, McGraw-Hill Education, chapters on present value and the opportunity cost of capital.