Savings calculator

Saving with regular deposits means setting aside the same amount every month, which then grows alongside everything you set aside before. The final amount is therefore not just the sum of your deposits: it also holds the return those deposits generated over the whole time.

The engine behind the whole calculation is compound interest. The return earned in a month is added to the balance and from the next month onward earns alongside it. You earn on what you have already earned, which is why the savings curve does not climb evenly but gradually accelerates. That is also why time, not the size of the deposit, is the variable that matters most.

Regular investing combines that effect with a second one: every month you add another deposit which begins earning a return of its own. Each deposit gets a different amount of time, though. The first works for the whole period, the last barely at all. A deposit postponed by five years therefore costs not only those few hundred euros but the entire growth it would have produced over those years.

This is why the result is worth reading as two numbers. Your deposits are the sum of what you actually sent to the account: the opening deposit plus the monthly deposit times the number of months. The return is the remainder, what the growth generated. Over a short horizon the deposits dominate; over a long one the ratio flips and the return outgrows everything you paid in.

The last pair of numbers is the nominal and the real value. The amount saved is nominal, the count of euros in the account. The real value is that same amount restated in today's prices, what it will actually buy. Prices rose in the meantime, so the real value is always lower, and the gap between them is exactly what inflation takes out of the result. Plan by the real value: the nominal figure looks generous, but after twenty years of inflation it corresponds to considerably less purchasing power.

The calculation has two independent parts that are added at the end. The first compounds the one-off opening deposit, the second handles the monthly ones. Both work with the monthly rate i = r/12 and the month count N = 12t, because the deposits arrive monthly and interest is credited just as often.

The initial deposit sits in the account for the whole period, so the exponent applies to it at full length. The power is the mathematical statement that interest is calculated on an already compounded amount.

Each individual deposit earns for a different length of time. Rather than adding two hundred and forty separate terms, the closed form of a geometric series gives the same answer in one calculation.

The factor k at the end settles something most calculators leave unsaid: when in the month you deposit. For a deposit at the end of the month k = 1, an ordinary annuity. For one at the start, every deposit earns a month longer, so k = (1 + i). The difference looks negligible at a glance, yet over a long horizon it is tens to hundreds of euros, and it is usually the reason two calculators disagree.

Inflation is quoted annually, so this step works in years rather than months. Dividing by the cumulative inflation factor converts the nominal amount into today's prices and so answers the question of what it will really buy.

The units matter. The most common mistake is confusing a percentage with a decimal; the second most common is confusing an annual rate with a monthly one.

The terms used in this calculation are explained in more depth in the encyclopedia.