Why money later is worth less than money now
Not because of inflation, although inflation makes it worse. Money in your hand can be put to work, so a pound promised for next year is worth only as much as the amount you would have to set aside today to end up with that pound. Discounting is that sentence turned into arithmetic, and the discount rate is what you assume the money would earn in the meantime.
Everything else follows from the rate. A low rate barely touches a distant sum; a high one can cut it in half over a few years. Since the rate is an assumption rather than a fact, the useful way to read this page is to try the rate you believe and then a rate either side of it, and see whether the decision you are making actually changes.
Two shapes of money, one answer
The form takes a single sum arriving at the end and a regular payment arriving every period, and you can use either on its own or both together. A settlement offer or a maturing bond is the first shape. A pension, a lease, a rental income or a set of instalments is the second. The answer breaks into those two parts underneath the total, because knowing which part carries the value tells you which assumption matters.
Payments at the start of each period are worth more than payments at the end, because each one has an extra period to earn. The difference is exactly one period of interest across the whole stream, and it is the difference between a lease paid in advance and one paid in arrears.
Reading the table
The last column of the table is not a running total. It is what everything from that period onwards is worth on that date, which is why the first row equals the answer and the last row equals the final payment. Read upwards and you can watch the value build as you get nearer the money; read downwards and you see how quickly the far end of the stream stops mattering, which is the real lesson of discounting at any serious rate.
Common questions
What discount rate should I use?
The return you could actually get on the same money at similar risk. For a business that is the cost of capital, and for a private decision it is usually the rate on the alternative you would genuinely take. A rate pulled from an article is a rate nobody is offering you. Where the number is contested, the useful move is to find the rate at which the decision flips and then argue about whether reality is above or below it.
Should I use a real rate or a nominal one?
Be consistent. Either discount the cash amounts as they will actually be paid at a rate that includes inflation, or restate every amount in today's money and discount at a rate with inflation stripped out. Mixing the two, which is easy to do without noticing, produces an answer that is wrong in a direction nobody can estimate.
Why is this page not the same as the compound interest calculator?
They model different things. The savings pages simulate an account: interest is earned every month and added to the balance on the compounding date you pick. This page values a stream of payments on a grid of equal periods, with the rate applied once per period. Where the rhythms coincide the answers agree; where they do not they differ slightly, and neither is an error.
Why does the total differ by a penny from my own calculation?
Because this page rounds to the cent once per period, as a real payment schedule does, while the textbook formula lets the value run to fractions of a cent throughout. Each period can move the answer by at most half a cent, so a long stream can drift by a few cents and a very long one by a little more; the tests hold it to half a cent a period. The version shown here is the one that adds up when the rows are totalled by hand.
Is anything I type stored?
No. The calculation happens on the server as part of rendering the page, nothing is written down, and the access log for this site drops the query string precisely so that the numbers you enter are never recorded.
Sources
No figure on this page is read from a table, so there is nothing to source. What these documents define is the convention behind the arithmetic, and the regulated measures this calculator deliberately does not compute:
How this is worked out
The figures are arithmetic on the numbers you type, and nothing here is a forecast of what an investment will actually do.
Money is held in whole cents and every step is integer arithmetic, so the same inputs always give the same answer. A period is discounted in one division, with the annual rate divided by the number of periods in a year inside the same expression, and the result rounded to the nearest cent. That means the answer is a cent or two away from the textbook formula, which lets interest run to fractions of a cent forever. The table on the page is the calculation itself rather than a second pass over it, so the rows and the headline can never disagree.
This page treats money as a stream of payments on a grid of equal periods. The compound interest and savings pages model a bank account instead, where interest is earned every month and added to the balance on the compounding date you choose. The two answers differ by a little when the paying-in rhythm is not the compounding rhythm, and neither is wrong: they are answers to two different questions.