Compound interest

Savings projection with monthly deposits. Free, no upload. 1 GB max · Up to 1 GB · Processed locally, never sent to a server.

Savings do not grow in a straight line. The interest earned in one period joins the capital and earns interest of its own in the next. This page projects that accumulation from four figures: an opening balance, a monthly contribution, an annual rate and a term of anywhere between one and sixty years.

The calculation runs month by month rather than year by year. The annual rate you type is converted into the equivalent monthly rate, applied to the running balance, and the month's contribution is then added on top. Three boxes give the final balance, the total paid in and the interest earned, while a table underneath breaks the projection down year by year, with cumulative contributions and cumulative interest side by side.

The projection assumes a constant return for the whole term. That is a calculation assumption and never a forecast: inflation, tax and fees play no part in the formulas used here, and a past return promises nothing. The formulas are spelled out below with the arithmetic of the default simulation, so every row of the table can be redone by hand or in a spreadsheet.

How to use it

  1. Set the opening balance The opening balance field accepts zero: a projection that starts from nothing and rests entirely on the monthly contributions is perfectly valid.
  2. Fix the monthly contribution This amount is added at the end of each month, twelve times a year, and never changes over the term. Leave it empty or at zero to watch the opening balance grow on its own.
  3. Enter the annual rate Set in steps of 0.1, it is understood as gross and constant. It really is an annual rate: the conversion to a monthly figure is done by the page, and it is not a division by twelve.
  4. Choose the term In years, from 1 to 60. Beyond a dozen rows the table stops printing every year and shows a regular sample instead, with the final year always kept visible so the end point can be read.
  5. Compare the three totals Final balance, total paid in and interest earned recalculate on every change. The gap between the first two is exactly the third.

The formula, and one complete example

With no contributions, the balance follows the classic formula: final balance = opening balance × (1 + rate)^term, with the rate as a decimal and the term in years. Once regular contributions are added, the future value of a series of deposits joins it, contribution × [(1 + i)^n - 1] ÷ i, where i is the monthly rate and n the number of months. The page adds the two terms together by walking through the months one at a time.

Take the default values: 1,000 to start, 100 a month, 5 percent a year, ten years. The equivalent monthly rate is 0.407412 percent. The opening balance becomes 1,000 × 1.05^10 = 1,628.89. The 120 contributions produce 100 × (1.628895 - 1) ÷ 0.00407412 = 15,436.32. Total: 17,065.21, against 13,000 that actually left your account and 4,065.21 of interest.

The total paid in includes the opening balance, which is why it reads 13,000 and not 12,000. The interest shown is simply the difference between the final balance and that sum, and the cumulative column in the table follows the same definition. After the first year the table already shows 2,200 paid in for a balance of 2,277.26, that is 77.26 of interest; after five years, 7,000 paid in for a balance of 8,057.66.

Simple interest and compound interest

Simple interest is always calculated on the original capital: 10,000 at 4 percent returns 400 every year, so 12,000 after five years. Compound interest is reinvested, so in the second year the 4 percent applies to 10,400, in the third to 10,816, and the same deposit reaches 12,166.53 at the end of the fifth year.

A gap of 166.53 over five years looks modest, and that is the point: it accelerates. Over long horizons the term is the most sensitive variable in the projection, ahead of the rate itself. Regular contributions work differently: they widen the base the return applies to, but each one works for less time than the one before, and a contribution made in the final year earns a single year of interest.

Why 5 percent a year is not 0.4167 percent a month

The conversion used here is the equivalent monthly rate, obtained with a twelfth root: (1 + 5/100)^(1/12) - 1 = 0.407412 percent. Compounded twelve times, it gives back exactly 5 percent over the year. Dividing 5 by 12 would give 0.4167 percent, a proportional rate whose compounding over twelve months produces 5.116 percent, so the advertised return would be quietly exceeded.

On the default simulation the gap between the two conventions reaches about 110 after ten years, and it widens with the rate and with the term. This page therefore uses the actuarial convention, the one that matches the annual rate a bank or a savings product advertises. The mortgage calculator on this site uses the other convention, the proportional one, because that is the convention written into credit contracts.

The contribution is added after the month's interest has been credited. A deposit therefore earns nothing in the month it is made: that is the end-of-period convention, the more conservative of the two and the one most projection tools apply. A beginning-of-period convention would give every contribution one extra month of growth.

What the projection leaves out

No tax is applied. Depending on the wrapper the money sits in, gains may be taxed as income, taxed at a flat rate, taxed only on withdrawal or not taxed at all: an ISA in the United Kingdom, a 401(k) or an IRA in the United States, a life policy in France all behave differently. The final balance shown is a gross figure.

Inflation is absent as well. A balance of 17,065 in ten years will not buy what it buys today. To reason in today's money, type a return already reduced by the inflation you expect. Entry charges, annual management fees and switching costs cut the result the same way and are not modelled either: a platform fee of one percent a year is a full point off the rate you should be typing.

A fixed return is finally a convenience. A regulated savings rate changes by decree, a fund publishes a different figure every year, and an equity portfolio can fall several years running before it recovers. The order in which good and bad years arrive changes the final balance even when the average is identical. The curve produced here is one theoretical path among many, and this page recommends no product and gives no financial advice.

Frequently asked questions

Why is the total paid in larger than the sum of my contributions?

Because it includes the opening balance. With 1,000 to start and 100 a month for ten years, the box shows 13,000, that is 1,000 plus 120 × 100. The interest box is then the final balance minus that same total.

Is the annual rate divided by twelve?

No. It is converted with a twelfth root, which gives 0.407412 percent a month for 5 percent a year. A balance left alone therefore lands on exactly the figure the annual formula predicts, to the cent, instead of drifting above it.

Does a contribution earn interest in the month it is made?

No. Each month the interest is credited first and the contribution is added afterwards. A deposit starts working the following month, which is the more cautious of the two usual conventions.

Why does the table skip years?

Past twelve rows it prints a regular sample rather than every year, so the table stays readable, and it always keeps the final year. The term itself is capped at sixty years, and a larger figure is brought back to that limit.

Are tax and inflation taken off the final balance?

Neither. The result is gross of tax and expressed in nominal terms. To approximate purchasing power, enter a real rate, that is the return you expect minus the inflation you expect.

Does the projection work for an equity portfolio?

It gives an average order of magnitude, nothing more. The calculation assumes an identical return every single month, whereas a market alternates rises and falls, and the sequence in which they arrive changes the final balance.

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