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📖 The story

Greg has been staking $20 a week on the lottery for years – about $85 a month. Had he invested that amount instead for 35 years at 6 %, a fortune would have grown.

ℹ Ordinary savings rate, no winnings considered.

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

What you learn

Small, seemingly harmless expenses add up over decades with compound interest into considerable wealth – the regular stake would have produced a real supplementary pension.

In short: The regular stake would have grown over the years into a considerable fortune – a strong advisory argument against spending habits.

Formula

FV = K0·q^n + R·(q^n − 1)/(q − 1), q = (1+i_eff)^(1/m)

With the example numbers

q = (1+0,0600)^1/12 = 1,004868, n = 35·12 = 420
FV = 85,00 €·(qⁿ−1)/(q−1) = 116.756,34 €

How to read the formula

Every installment earns interest until the end – early installments longer, late ones shorter. The bracket (qⁿ−1)/(q−1) sums up all these differently compounded contributions at once. q is the growth factor per period: from the effective rate p.a. the matching monthly factor is derived via the ¹ᐟᵐ root. Takeaway: it is not the sum of the deposits that counts, but how long each dollar is allowed to work.

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