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El Cerebro

Investment

Compound interest with inflation

What the money you save will be worth in a few years, counted twice: in euros of the time and in today's euros.

What it does

It projects an initial capital to which a constant monthly contribution is added over a number of years, assuming an annual return that compounds every month. It then applies the inflation of the period to the final value: the large figure is the nominal value and the detail shows what that same amount would be worth in today's euros.

Key concepts

  • Compound interest: the return is added to the capital and, from then on, also generates return. Each period applies its balance on top of that of the previous period, and that is why growth is not a straight line but a curve that accelerates.
  • Monthly compounding: the annual return is divided by twelve and applied once a month. With an annual 6 % the monthly rate is 0,5 %, not 6 %: that division is the difference between a reasonable figure and one inflated twelve times over.
  • Contribution at the end of each month: the contribution goes in at the close of the month, so the first one only grows for the months that remain. It is the convention of an automated contribution plan, and the one this calculator uses.
  • Nominal value and real value: the nominal value is the figure in euros of that future moment; the real value discounts inflation and tells you how many euros of today would have the same purchasing power. The longer the term, the further apart the two figures move.
  • Accumulated interest: the difference between the final value and everything that was contributed. It is the part of the balance that comes from the return and not from the savings.

Frequently asked questions

Where do the numbers come from?

The return and inflation are two assumptions that whoever uses the calculator types and can change at any time. They are not a forecast, they are not a recommendation and they are not market data: the result is what happens with those numbers, not what is going to happen.

How is compound interest calculated?

By applying one period's rate to the previous balance and adding the result to that balance, over and over. With this calculator's monthly compounding, the balance in month k is that of month k-1 multiplied by 1 + r/12/100, and the month's contribution is added afterwards, at the end.

Why does the first contribution grow less than the last one?

Because all contributions go in at the end of their month. In a ten-year plan, the first contribution compounds for 119 months and the last one for zero, so the sum of the contributions does not behave like any lump sum.

What happens if the return is zero?

The general formula divides by the monthly rate, and with a zero rate that division does not exist. The calculator then uses the simple sum, capital plus contributions, which is the correct result in that case and not a typing error.

What is the difference between the final value and the value in today's euros?

The final value is nominal: the figure the balance ends at in so many years. The value in today's euros deflates that amount by the inflation of the period and answers a different question: how many euros of today would have the same purchasing power as that future amount.

How is inflation deducted?

The final value is divided by the accumulated inflation factor of the period. Inflation of 2 % a year over ten years is worth an accumulated factor close to 1,22.

Are percentages written with the % symbol?

No. The return and inflation are entered as numbers: 6 means 6 %. If you write "6 %", 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 initial capital runs from 0 to 10.000.000 €, the monthly contribution from 0 to 100.000 €, the return from −99 to 100, inflation from −10 to 100 and the term from 1 to 80 whole years. An empty field does not equal zero: leaving it blank and typing 0 are two different intentions.

Does the account round the results?

No. The calculation keeps all of its decimals and the rounding happens when the figures are presented. Intermediate rounding would give prettier and false amounts: in a series of eighty points, a cent of difference shows.

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