📖 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.
Topics › Leasing, Credit & Consumption › Play or save?
Easy
Leasing, Credit & Consumption
Play or save?
Change any number and press "Calculate" – or use "Type in" on the right to watch it entered step by step.
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 $
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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