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El Cerebro

Saving and planning

Savings goal: how much to contribute each month

The monthly amount needed to reach a specific figure within a specific period, calculated with the assumptions that are entered.

What it does

It starts from a savings goal, an initial capital, a number of years and an assumed annual return, and solves for the constant monthly contribution that takes the balance to the goal. It also shows the total contributed and the part of that total that corresponds to interest, and draws the path of the balance alongside the goal line.

Key concepts

  • Constant monthly contribution: the unknown of the account. It comes from the future value equation, imposing that the final balance be the goal, instead of calculating backwards year by year.
  • Monthly compounding: the annual return is treated as a monthly rate, the annual rate divided by twelve, and it is applied for 12 months for each year of the term. It is the same convention as the rest of the calculators in this catalogue.
  • Estimated interest: the difference between the goal and the total contributed. It is an estimate made with a constant, assumed return, not a forecast of what is going to happen.
  • Goal: the target figure. The calculator treats it as data, without adjusting it for inflation or to any specific moment.
  • Term: the number of years until the goal. It is the figure that weighs most heavily on the result: lengthening the term lowers the monthly contribution even though the total contributed rises.

Frequently asked questions

Where do the numbers come from?

The goal, the term and the return are figures that whoever uses the calculator types. The return is a modifiable assumption, not a forecast, and the resulting contribution is only valid for that set of numbers.

How is the required monthly contribution calculated?

It is solved from the future value equation of an annuity: A = (M − P · (1+m)^N) · m / ((1+m)^N − 1), where M is the goal, P the initial capital, m the monthly rate and N the number of months. If the return is zero, that expression does not exist and the split is equal: A = (M − P) / N.

What happens if the initial capital already reaches the goal?

The account comes out negative, and the calculator takes it to zero instead of showing a negative amount. The label of the figure then changes to "You already reach the goal with what you have", because negative savings are not a savings plan.

What is the difference between total contributed and estimated interest?

The total contributed is the sum of everything entered: the initial capital plus the monthly contribution over the number of months. The estimated interest is what the assumed return has added to the balance, that is, the goal minus that total contributed.

Why does the contribution come out with so many decimals?

Because the account does not round. Rounding in the calculation would give a prettier and false figure: the final balance would end up a few cents below the goal, and that shortfall would show in every year of the chart.

Are percentages written with the % symbol?

No. The return is entered as a number: 4 means 4 % a year. If you write "4 %", the field is flagged as invalid and the figure disappears, instead of the calculator correcting the figure on its own.

What limits do the fields accept?

The goal and the initial capital run from 0 to 10.000.000 €, the term from 1 to 80 whole years and the return from −100 to 100. An empty field does not equal zero: leaving it blank and typing 0 are two different intentions and the calculator cannot know which one it is.

And if the return is negative?

The formula allows for a negative return, and then the balance stops growing or shrinks. The monthly contribution needed to reach the goal rises accordingly, and if with those numbers the goal falls out of reach the figure reflects that instead of clipping it.

Does the goal take inflation into account?

No. The account works in current euros: the goal and the initial capital are amounts of today and the return you enter is nominal. To read that result in today's purchasing power you have to deflate it, which is what the compound interest calculator does.

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