Compound Interest Growth Calculator

The money you are starting with, before any monthly contribution. Zero is allowed as long as you are contributing something; with neither, there is nothing to grow and the status line says so.

Optional. What you add every month. Leave it blank for a lump sum left alone, which is the commonest case and is what this workbook ships showing. Contributions are monthly whatever compounding frequency you choose, because that is how standing orders work.

How long the money is invested. The monthly schedule covers fifty years, which is the limit the status line states. The answer is more sensitive to this than to anything except the rate, because the last years of a long run carry most of the growth.

How unsure you are of the annual rate, as one standard deviation. This is as much a part of the answer as the rate itself, which is why it is asked for rather than assumed. Quote it PER YEAR: the model applies one constant rate across the whole run, so the figure is scaled to the horizon by the square root of time, because a long-run average is less uncertain than a single year. A savings account whose rate is fixed is near zero; a diversified equity portfolio is nearer fifteen percent. Set it to zero to say you are certain, and the grid collapses onto your own figure.

Optional. How fast prices rise. It changes nothing about the balance; it converts the answer into what it would buy today, which is the only form in which a figure thirty years out means anything. Leave it blank and the real-terms line stays blank rather than quietly assuming zero.

The rate as it is quoted to you, per year, before it is compounded. This is a nominal rate, not the effective one: an account advertising five percent compounded monthly is quoted five percent here, and the effective annual rate it really pays is reported below. Held constant for the whole run, which is the assumption the grid at the foot exists to question.

Optional. How much the monthly contribution rises each year, on the anniversary rather than smoothly. A contribution that never rises is one that shrinks in real terms every year, and raising it with your pay is both commoner and materially different. Leave it blank and the contribution stays flat.

Whether the monthly contribution arrives at the start or the end of each month. Money paid at the start earns one more period of interest, which is worth a little over a long run and is the difference between two tools that otherwise look identical.

How often the interest is actually added to the balance. It is the difference between a rate and a return: the same five percent is worth more added daily than added once a year, and continuous compounding is the limit that more and more frequent adding approaches. Choose what the account or the quote actually does, not what is convenient.

Machinery. Excel requires the formula being tabulated to sit in the grid's top-left corner, where it means nothing to a reader, so it is formatted away. It holds Final_Balance.

The values down the left of the grid: the annual rate, spread either side of your own figure by half a standard deviation a row, after scaling your yearly uncertainty to the length of the run. Read a row to hold the rate fixed and vary the horizon. The middle entry is your own figure, never clamped.

Machinery, and NOT an input. The same for the column axis: Excel substitutes each horizon into it while filling the grid, and the rest of the time it mirrors Years_Invested.

What the same money would reach if the interest were paid out rather than reinvested: the starting amount growing by the quoted rate on itself alone, with the contributions added back at face value. Nobody is offered this; it is here as the baseline that makes the next line mean something.

The values across the top of the grid: how many years the money is invested, in plain steps of a tenth of your own horizon, at least one year apart. Nothing here carries a probability, because how long you invest is a decision rather than an outcome. The middle entry is your own figure.

The starting amount plus every contribution: all of the money that is yours rather than the account's. Reading it against the final balance is the quickest way to see how much of the answer is compounding.

How long the money takes to double at the effective annual rate, which is what the rule of 72 approximates. Blank at a zero rate, where nothing doubles.

Every monthly contribution added together, at face value with no interest. Zero when no contribution is entered.

Machinery, and NOT an input. Excel substitutes each value from the row axis into this cell while it fills the grid; the rest of the time it mirrors Annual_Return. Change Annual_Return above, never this: the axis is derived from it, so editing the mirror moves the axis while the table walks and the grid comes out meaningless.

The body of the grid: the final balance, recomputed for every combination of the two axes. One hundred and twenty-one cells, each one the whole projection run again. It is a component of the table rather than a result on its own.

The final balance restated in today's money at the inflation rate you entered. Blank until you enter one, because a real-terms figure with no inflation assumption behind it would be the nominal figure wearing a different label.

The final balance less the simple-interest balance. This is what compounding is worth in dollars, and over decades it is usually larger than the whole of the interest a simple account would have paid.

What the quoted rate really pays over a year once the compounding is counted, sometimes called the APY. Seven percent compounded monthly is 7.2290 percent a year; compounded continuously it is 7.2508. This is the figure to compare two quotes on, and it is the one most calculators never show.

The balance in a lucky tenth of the rates. The distance between this and the unlucky tenth is the honest width of the answer, and on a thirty-year run it is usually a multiple rather than a margin.

The balance in an unlucky tenth of the rates on the grid: the run where the average annual rate comes in well below the figure you entered. If the gap between this and the headline figure is uncomfortable, the headline figure was never the answer.

The middle of the weighted rates. It sits BELOW the headline figure rather than on it, and that is not a defect: the balance rises faster than the rate does, so the average of the outcomes is pulled above their middle. The centre cell of the grid is the one that must match the headline exactly, and an invariant asserts it.

The final balance less every dollar you put in. On a long run at a decent rate this is the larger half, which is the point of the tool.

Reads OK, or explains why the inputs are not valid or why the answer deserves a second look.

What the monthly contribution has grown to by the end, if you set it to rise each year. It is the figure you would pay in the month after the last one, so a contribution of 400 rising three percent a year for thirty years ends at 970.90. Equal to the contribution entered when it does not rise, and zero when there is no contribution at all.

The same rate expressed per month, which is the rate this model actually walks the schedule at. At monthly compounding it is exactly the quoted rate over twelve; at any other frequency it is the monthly rate that compounds to the same annual figure.

What the balance reaches at the end of the run, including every contribution and all the interest. It is the cell the grid at the foot recomputes, so the middle cell of that grid must equal this figure exactly.