Savings rate for the desired pension

📖 The story

32-year-old David has 35 years until retirement and wants to build up $360,000 by then to afford a supplementary pension later. He assumes 7 % return.

ℹ Ordinary savings rate, no starting capital.

Change any number and press "Calculate" – or use "Type in" on the right to watch it entered.

What you learn

Good news for young savers: with a long horizon a surprisingly small rate is enough for a big goal – every year earlier lowers the necessary savings rate further.

In short: With a long investment horizon a surprisingly small monthly rate is enough to build a large target amount.

Formula

R = (FV − K0·q^n) / ((q^n − 1)/(q − 1))

With the example numbers

R = 360.000,00 € / ((qⁿ−1)/(q−1)), q = 1,005654, n = 420 = 210,35 €

How to read the formula

Here the final-value formula is solved for the rate: you divide the target by the compounding factor (qⁿ−1)/(q−1), which shows the multiple to which a rate of $1 grows. Takeaway: the longer n, the larger this factor – and the smaller the rate needed.

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