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Compounding means this year's growth earns growth of its own next year, which is why the line bends upward instead of running straight. The return you enter is an average, not a promise: real markets deliver it as a jagged series of good and bad years, and the order those years arrive in matters if you are withdrawing. Contributions are counted at the end of each period, which is the conservative assumption; paying yourself first at the start of the month adds a fraction of a percent. Buying power strips inflation back out so the ending balance is stated in what it would buy today.

This runs the compounding sum backwards: you name the finish line and it returns the deposit. For a goal inside about five years, keep the rate low and the money somewhere it cannot fall, such as a high yield savings account, since a market dip right before the deadline is not something a short timeline can recover from.

An emergency fund is measured in months of spending, not in a round number of dollars, so it is built from the bills that do not stop when income does. Count only the essentials: the target is survival, not your current lifestyle. Three months suits a stable salary with a second income in the house, six to twelve suits variable pay, self employment or a single income.

Banks advertise APY, which already includes compounding, and lenders quote APR, which does not. This shows both from the same rate so the difference is visible. A CD locks the rate for the full term, which protects you if rates fall and costs you if they rise, and cashing out early usually forfeits several months of interest.

Total return answers how much you made. Annualized return answers how fast, which is the only fair way to compare a holding of six months against one of ten years. Doubling your money sounds identical in both cases and is a very different investment. Costs and dividends are both included here because leaving either out flatters the number.

A fee is charged on the whole balance every year, and the money it removes would otherwise have compounded for every year that remained. That is why a percentage that looks trivial takes a double digit share of the final balance. Index funds commonly charge under 0.10%, actively managed funds ten times that, and a percentage based adviser adds around 1% on top.

The headline return on an investment is the least useful of the three numbers here. Tax removes a share of the growth, and inflation removes a share of what is left, so a return that sounds healthy can leave you barely ahead. The correct arithmetic divides rather than subtracts: a 7% return with 3% inflation is 3.9% of real growth, not 4%. Tax is modelled as a yearly haircut on the return, which is what an ordinary brokerage account with some turnover looks like; if you buy and hold for decades the tax lands once at the sale and the real figure is a little better than this. State tax, fund fees and trading costs are not included, and the inflation rate that matters to you is the one on the things you actually buy, not the national average.

Dividing 72 by a return gives a doubling time you can work out in your head, which is the whole reason it exists. It is an approximation of the real answer, the natural log of 2 divided by the log of one plus the rate, and 72 is used instead of the mathematically tidier 69.3 because it divides cleanly by 2, 3, 4, 6, 8, 9 and 12. The shortcut is close between about 6% and 10% and drifts steadily wider outside that band, which is why the exact figure sits beside it here. Neither number allows for tax, fees or inflation, and doubling your money in nominal terms while prices also double leaves you exactly where you started.

The same rate can be printed two ways. A nominal rate, which banks label APR, is the yearly rate before compounding is counted. An effective rate, labeled APY on a savings product, is what the account actually pays over a year once the interest has itself started earning interest. Savings accounts advertise the larger of the two and loans advertise the smaller, which is not an accident. The gap is small at ordinary rates and grows quickly at high ones, which is why credit card maths gets ugly. Loan APR also folds in some fees by law, so a real loan quote is not a pure interest rate, and none of this includes tax on the interest you earn.

Reinvesting turns each dividend into more shares, and those shares pay dividends of their own, which is where the curve comes from. The two paths here are taxed identically, because the IRS does not care whether a dividend was reinvested: it is income in the year it is paid either way, unless the account is an IRA or a 401(k). What separates them is only what happens to the money afterwards. The cash path assumes the money is spent or left idle, so if you invest it somewhere else the gap narrows. Dividend growth and price growth are typed in as smooth yearly figures, and real companies cut dividends in bad years, which is exactly when a smooth model looks most convincing.

Dollar cost averaging means investing a fixed amount on a fixed schedule instead of all at once. It buys more shares when prices are low and fewer when they are high, and it removes the decision of when to start. What it cannot do is beat a rising market, and markets rise more often than they fall: historically, investing a lump sum immediately has finished ahead of spreading it out roughly two thirds of the time. This calculator will always agree with that as long as the return you type is above the rate on the waiting cash, because it has no volatility in it at all. The real case for spreading it out is not the arithmetic, it is that a 30% drop the month after you commit everything is the kind of thing that makes people sell at the bottom.

A portfolio drifts because its parts grow at different speeds, and drift is not neutral: after a long run in stocks you are holding more risk than you chose, usually right before you find out. Rebalancing sells what has done well and buys what has not, which feels wrong and is the point. In a taxable account each sale realizes a gain and a tax bill, so directing new money and dividends into whatever is light is the cheaper way to do the same job, and that is what the extra cash field is for. Rebalancing bands, such as acting only when something drifts five points from target, cut the trading down without letting the portfolio wander far. Nothing here accounts for tax, trading costs or the wash sale rule.

Allocation is the decision that explains most of what a portfolio does. Stocks carry the return and the falls, bonds soften the falls and pay less, cash does neither and is there so you never have to sell anything at a bad moment. The return figures below are US averages measured over nearly a century, and a single decade can look nothing like them: stocks returned roughly nothing from 2000 to 2009 and bonds had their worst year on record in 2022. The bad year estimate blends the worst calendar year each asset has had, which is a rough stand in for risk and not a floor; a mix can fall further than that, and 1931 was far worse for stocks than 2008. The suggested mix is a rule of thumb keyed to your age, not advice, and it ignores your job security, your other assets and how you actually behave when the number drops.

Cost basis is what you paid, and it is the number the gain is measured against when you sell, so it is worth keeping right. Commissions and fees are part of it, and reinvested dividends are too: each reinvestment is a new purchase at that day's price, which is why people who never sold anything still owe tax on a fund they have held for years. The average price shown here is a portfolio summary, not a tax method. Mutual funds may use average cost, but individual shares are sold either first in first out or by naming the specific lot, and naming the lot with the highest basis is usually the cheaper way to sell. A gain is unrealized until the sale, and unrealized gains cost nothing.

A bond's coupon never changes, so when its price moves the yield moves the other way: pay less than face value and the same coupon is worth more as a percentage, plus you collect the difference back at maturity. Current yield only counts the coupon against the price. Yield to maturity counts the pull back to face value as well, which is the number worth comparing against another bond. The headline here uses the standard approximation, which spreads the discount or premium evenly across the remaining years, and it runs a fraction of a percent off the true figure on long bonds; the exact solved yield sits beside it. Coupons are treated as annual, while most US bonds pay twice a year, and the whole calculation assumes the issuer pays and that you reinvest the coupons at the same yield. Neither is guaranteed.