A small child approaches his father, who provides him a modest allowance each month:
“Hey, dad, how about, instead of giving me my normal allowance of $25 per month, you give me 1 penny the first day, and double it each day for the month?”
“OK.”
Dad didn’t “do the math.” Read it and weep, pops:
Theoretically, this could work out well for the kid (but then again, everything works in theory). By the twelfth day, they have exceeded their previous allowance of $25 per month; by the seventeenth day, they’ve racked up more than a thousand dollars; by the twenty-seventh day, they’ve become a millionaire; and at the end of a normal month (not February), they’ve accumulated a cool ten or twenty million dollars.
Who says it doesn’t pay to learn math?
Even if they started over at the beginning of each month at the rate of a penny per day, doubling it each day, in a normal (non-leap) year, the kid would “earn” almost 200 million dollars ($195,957,882.76, to be precise). This figure is calculated by adding together the single 28-day month at $2,684,354.55 plus the four 30-day months at $10,737,418.23 each plus the seven 31-day months at $21,474,836.47 each, to reach that total of $195,957,882.76.
For this to really succeed, though, three things (alas!) have to be true:
1) Their dad has to fall for it (he just goes with his gut instinct that doubling a penny 30 times can’t amount to much)
2) He is a multi-millionaire and can afford to pay it
3) He honors his agreement, and forks over the agreed-upon sum, even though he was “bamboozled”
If all those conditions exist, the kid could retire (quite) young. Being the compassionate and caring child that they are, they could easily afford to build a modest guest cabin on the back forty for their poor beleaguered parents, and show pity on them in their straitened circumstances by hiring them as their housekeeper and groundskeeper (of course, their mother will be the groundskeeper and their father the housekeeper — after all, this is 2022, not 1952).