savingsmathEvery term the calculators use, plus FIRE terms and fund abbreviations, in plain words. Many come with a side-by-side example that shows what changing one value does. Educational only, not advice.
Your money earns a return, and next year that return earns a return too.
Each year the growth is added to your balance, so the base keeps getting bigger. It looks slow at first and fast later, which is why time matters more than anything else.
Difference: Three times as long, but almost nine times as much: the extra 376,868 is mostly interest on interest.
Compound annual growth rate: the steady yearly return that turns a start value into an end value.
It smooths good and bad years into one number. It says nothing about how bumpy the ride was in between.
Example: 10,000 that became 20,000 in 9 years grew at a CAGR of about 8% a year.
Try it in the calculatorLatin for "a year": a rate given p.a. is the rate for a whole year.
Savings accounts and bonds quote their interest p.a. When interest is added more often than once a year, what you earn in a year is a little higher; see the effective annual rate.
Example: 3% p.a. on 10,000 is 300 in a year when interest is added once a year, and about 304 when it is added monthly.
Try it in the effective annual rate calculatorWhat a rate really earns in a year once interest on interest within the year is counted.
APY (annual percentage yield) is the US name, AER (annual equivalent rate) the UK one. It lets you compare accounts that add interest monthly, quarterly or yearly.
Example: 5% a year added monthly is an effective 5.12% a year.
Try it in the effective annual rate calculatorThe part of your balance that came from earlier growth, not from your own money.
The calculator shows it separately in the chart and the money flow. Over long periods it becomes the biggest part of the pot.
Example: 10,000 at 10% earns 1,000 in the first year. In the second year it earns 1,100: the extra 100 is interest on interest.
Try it in the calculatorHow much your money grows in a year, as a percentage.
For a savings account it is the interest rate. For funds it is an average of years that go up and down; the calculator uses one steady number to show the idea.
Difference: A bit more than double the return gives about four times the result: 321,883 more.
The money you put in once, at the very beginning.
It has the most time to grow, so even a modest starting amount can end up as a large part of the result.
Difference: The 10,000 alone grows into 198,374.
The money you add regularly: every day, week, month, quarter or year.
The calculator turns any period into a monthly amount. What you put in is shown in blue, what it earned in gold.
Difference: An extra 100 a month, 36,000 over 30 years, adds 226,049.
How often growth is added to your balance so it can start growing too.
More frequent compounding adds growth sooner. The yearly return you enter is split into equal parts, one for each compounding period.
Difference: Adding growth every month instead of once a year adds 43,644.
Whether each deposit arrives at the start or the end of its period.
A deposit at the start of the month grows for that month too. The difference is small but grows with time.
Difference: One extra month of growth on every deposit adds 1,884.
Cost averaging: putting in the same amount at regular times, whatever the price.
A fixed amount buys more shares when prices are low and fewer when they are high, so the average price you pay is never above the average of the prices. It does not remove market risk.
Example: Investing 100 a month: at a price of 50 it buys 2 shares, at 25 it buys 4. That is 6 shares for 200, about 33.33 each, while the average price was 37.50.
Try it in the calculatorInvesting a larger amount all at once instead of spreading it over time.
Because markets rise more often than they fall, money invested at once has usually ended ahead of the same money spread over months, but not always: a fall soon after hurts it more. Spreading it out (DCA) can make the start easier to live with.
Example: 12,000 invested in January has the whole year to grow; 1,000 a month has on average about half a year.
Try it in the calculatorHow many times bigger a part of your money became.
The calculator shows it for every 1 you put in, your starting amount and your savings. A starting amount has longer to grow, so its multiple is higher.
Example: 10,000 that grows to 198,374 grew about 19.8 times.
Try it in the calculatorThe year when your growth so far passes the total you have paid in.
After that point your money does more of the work than you do. The chart marks the year.
Example: With 10,000 to start and 100 a month at 10%, it happens in year 9.
Try it in the calculatorA quick way to estimate how long money takes to double.
Divide 72 by the yearly return in percent. It is a rough guide that works best between about 4% and 12%.
Example: At 8% a year, 72 ÷ 8 = 9, so 1,000 becomes about 2,000 in 9 years.
Try it in the calculatorPrices rising over time, so the same money buys less later.
Switch inflation on and the calculator shows every amount in today's money, so you can compare it with prices you know now.
Difference: The same pot buys about 222,082 less than its number suggests.
Money kept aside, easy to reach, for job loss, repairs or illness.
A common rule of thumb is 3 to 6 months of spending, kept in a savings account rather than invested, so you never have to sell investments after a fall.
Example: Spending 1,200 a month, 6 months is 7,200. Saving it in 2 years at 3% a year takes about 291 a month.
Try it in the savings goal calculatorA future amount converted to what it would buy today.
Your statement will show a bigger number in the future. Today's money divides it by how much prices rose, so you see its real buying power.
Example: 100,000 in 20 years with 2.5% inflation buys about what 61,000 buys today.
Try it in the calculatorYour deposit grows each year by the inflation rate, so it keeps its value.
If your income rises with prices, raising what you save keeps your plan on track. The calculator shows both results in today's money.
Difference: Keeping deposits in step with prices adds 25,550 in today's money.
A yearly charge a fund takes from your money, as a percentage.
TER means total expense ratio; it is also called ongoing charges (OCF) or, in the US, the expense ratio. It is taken every year from the whole balance, so over decades it adds up to much more than it looks.
Difference: A fee 0.8 percentage points higher costs 73,162 over 30 years.
A one-off charge when you buy into a fund or sell out of it.
An entry fee is taken from each deposit before it is invested; an exit fee from what you take out at the end.
Example: A 2% entry fee on 100 means 98 is invested.
Try it in the calculatorA share of the gains some funds keep for themselves.
It is charged on the growth, not the balance, and only some actively managed funds have it. Broad index funds usually do not.
Example: A 20% performance fee on 1,000 of growth takes 200.
Try it in the calculatorHow far a fund's yearly return falls behind (or ahead of) the index it follows.
It is the cost you actually feel. It is often close to the TER, but trading costs, tax on dividends and income from lending shares can make it larger or smaller.
Example: The index rose 8.0% in a year and the fund 7.8%: the tracking difference is −0.2 percentage points.
A short standard document every fund sold in the EU must give you before you invest.
Under the PRIIPs rules it has at most three pages and shows what the fund does, a risk score from 1 to 7, scenarios of possible results and the costs in money and in percent. The older version for UCITS funds was called a KIID.
Example: A KID shows, for example, what costs would take from 10,000 invested over the recommended holding period, both in money and as a percentage a year.
Tax on what your money earned, not on what you put in.
Rates and rules depend on your country and account. The calculator uses one rate you choose; it is an estimate, not tax advice.
Example: With 19% tax, 1,000 of growth leaves 810.
Try it in the calculatorTwo ways tax on gains can work, depending on your account and country.
Taxed every year takes tax from each year's growth, so less is left to compound. Taxed when you sell lets the full amount grow and takes tax once at the end.
Difference: Paying tax every year instead of once at the end leaves 87,761 less.
A fund that holds all the shares of a market index instead of picking some.
Because it follows the index rather than trying to beat it, its fees are usually low. Its value goes up and down with the market.
Example: A world index fund can hold over 1,000 large companies from many countries.
An exchange-traded fund: a fund you buy and sell on a stock exchange, like a share.
Many index funds are ETFs. Costs include the fund fee and whatever your broker charges for trading.
Example: Buying one share of an ETF priced at 100 gives you a small piece of everything the fund holds.
Loans to governments or companies that pay interest and return the amount at the end.
They usually swing less than shares and grow less over long periods. Their prices still move when interest rates change.
Example: A 1,000 bond paying 4% a year pays 40 a year and returns the 1,000 when it ends.
An EU rulebook for funds sold to ordinary investors; most European ETFs carry it in their name.
UCITS funds must spread their money, keep it with a separate custodian and publish a KID. The rules limit the risk of one company; they do not protect you from the whole market falling.
Example: A UCITS fund may put at most 10% of its money in shares of one company, and holdings above 5% may together make up at most 40%.
International Securities Identification Number: a 12-character code that names exactly one security or fund share class.
Share classes of the same fund (accumulating, distributing, another currency) have different ISINs, so the ISIN is the surest way to find the exact one at your broker.
Example: An ISIN has 2 letters for the country, 9 characters for the security and 1 check digit, such as IE followed by 10 more characters for a fund from Ireland.
The value of everything a fund holds, minus its debts, divided by the number of its shares.
Fund prices are based on it. An ETF trades on the exchange during the day at a price that is usually very close to its NAV.
Example: A fund holding 50,000,000 with 1,000,000 shares has a NAV of 50 per share.
A part of a company's profit paid out to its shareholders.
A fund collects the dividends of the companies it holds and either pays them to you or reinvests them. Dividends are often taxed, depending on your country.
Example: A share priced at 100 that pays 3 a year has a dividend yield of 3%.
An accumulating fund reinvests the dividends it receives; a distributing fund pays them out to you.
Both hold the same things. They differ in when you receive money and how it is taxed, which depends on your country's rules and can change; this is not tax advice, so check the current rules or ask a tax adviser. The calculator assumes returns are reinvested, as in an accumulating fund.
Example: A fund worth 10,000 receives 2% in dividends: a distributing fund pays you 200 (before tax), an accumulating fund adds the 200 to the fund, so your shares are worth more.
Bringing a mix of investments back to the shares you chose, after some parts grew faster.
Without it, a plan drifts toward whatever rose most, usually shares, and carries more risk than you chose. Many people rebalance once a year, or put new deposits into the part that fell behind.
Example: A 60/40 plan grows to 7,500 in shares and 4,000 in bonds (65/35). Moving 600 from shares to bonds brings it back to 6,900 and 4,600.
Holding part of your money in index funds and part in bonds, such as 60/40.
The calculator mixes the two returns by their shares. More bonds usually means smaller swings and a smaller result.
Difference: A 60/40 mix grows to 189,883 less in this steady illustration, in exchange for smaller swings in real markets.
Fund values go up and down, so the result can land above or below a steady line.
A steady yearly return is a simplification. Real markets have good and bad years, and the order of them matters most close to when you need the money.
Example: A fund averaging 7% might rise 20% one year and fall 15% the next.
The middle outcome of many possible paths, and the band where most of them land.
Half of the paths end above the median and half below. A range from the 10th to the 90th percentile leaves out the 2 best and 2 worst in every 20.
Example: A median of 400,000 with a range of 250,000 to 650,000.
Spreading money over many investments so one failure cannot sink the whole pot.
It reduces the risk of single companies, sectors or countries. It does not remove market risk: when the whole market falls, a spread pot falls too.
Example: If one company in a fund holding 1,000 companies in equal parts goes bankrupt, the fund loses about 0.1%. If it was your only share, you lose all of it.
How far an investment falls from its highest point before it recovers.
The largest drawdown shows the worst stretch you would have had to sit through. Recovering needs a bigger rise than the fall: after −50% it takes +100% to get back.
Example: A pot that grows from 10,000 to 15,000 and then falls to 9,000 has a drawdown of 40%, though it is only 10% below where it started.
The risk that bad years come at the worst time: just as you start taking money out.
For a single amount you never take money from, the order of good and bad years does not change the end result. Once you withdraw, early losses force you to sell more shares at low prices, and the pot may not recover. That is why the 4% rule is a rule of thumb, not a guarantee.
Example: Two pots of 360,000 with the same average return: the one that falls 30% in the first year of withdrawals can run out years earlier than the one that falls 30% in year 20.
The pot you would need to live on its income: 25 times a year of spending.
It comes from the 4% rule, so it is also called the 25x rule. FIRE means financial independence, retire early, and this amount is often called the FIRE number.
Example: Spending 1,200 a month is 14,400 a year, so the target amount is 360,000.
Try it in the retirement calculatorTake 4% of your pot in the first year, then the same amount raised with prices.
US studies of past markets found this usually lasted 30 years or more. It is a rule of thumb from history, not a promise.
Example: From a 360,000 pot, 4% is 14,400 a year, or 1,200 a month.
Try it in the retirement calculatorMoney you take out of your pot to live on.
In retirement the pot keeps growing while you take money out. Whether it lasts depends on how much you take and how it grows.
Example: Taking 1,200 a month from a pot that grows faster than that can last for life.
Try it in the retirement calculatorThe age at which the pot would run out with your planned spending.
The retirement calculator follows your pot year by year until it is empty, or until age 100.
Example: A pot that pays 1,500 a month from 60 might run out at 84.
Try it in the retirement calculatorA movement of people who save and invest a large share of their income to stop depending on a salary years before the usual retirement age.
Financial independence means your investments could cover your spending. The usual target is 25 times a year of spending (the FIRE number), from the 4% rule, which is a rule of thumb, not a guarantee.
Example: Spending 1,200 a month makes the FIRE number 360,000. Starting at 30 with 10,000 and saving 300 a month at 7% a year reaches it at about 58.
Open "When can I retire?"Having enough invested that it could grow into your retirement target by itself, with no more saving.
From then on your income only has to cover today's spending. The amount depends on how many years the money has to grow and on the return you assume; we use 5% a year after inflation.
Example: At 30, to have 360,000 at 65 you would need about 65,300 invested today, at 5% a year after inflation.
Try it in the Coast FIRE calculatorFIRE on a small budget: a lower target because you plan to spend little.
It reaches independence sooner, but leaves less room for surprises such as higher rent or health costs.
Example: Spending 800 a month is 9,600 a year, so the target is 25 × 9,600 = 240,000.
Open "How much do I need to retire?"FIRE with a generous budget: a much higher target to keep a comfortable lifestyle.
It takes longer to reach, but the bigger pot leaves more room for travel, help for family or unexpected costs.
Example: Spending 5,000 a month is 60,000 a year, so the target is 25 × 60,000 = 1,500,000.
Open "How much do I need to retire?"Leaving full-time work while a part-time job still pays part of your spending.
The pot only has to cover what the job does not, so the target is smaller. The name comes from part-time work such as in a café, in the US partly for the health insurance it brings.
Example: Spending 1,200 a month with 600 from part-time work leaves 600 for the pot: the target is 180,000 instead of 360,000.
Open "How much do I need to retire?"The share of your pot you take out in the first year, then raise with prices, with a good chance that it lasts.
The 4% rule is the best-known one; for retirements longer than 30 years many people use 3 to 3.5%. "Safe" means it held in most periods of past markets, not that it is guaranteed.
Example: From 360,000, 4% is 1,200 a month; 3.5% is 12,600 a year, or 1,050 a month.
Try it in the retirement income calculatorThe share of your income after tax that you save or invest.
For FIRE it matters more than the return: a higher rate means more saved and less spending to replace.
Example: Earning 1,700 after tax and saving 500 is a savings rate of about 29%, leaving 1,200 to spend. Starting at 30 with 10,000 at 7% a year, that reaches the 360,000 target at about 53; saving 300 would take until 58.
Open "When can I retire?"