How A Math-Whiz Kid Asks For An Allowance

Parents, suppose your child approaches you and asks for an allowance, subject to the following conditions:

1. The child will do all dishwashing, vacuuming, and outside yard work for one year.  Yard work includes mowing, weed-eating, and gardening.  You won't have to do any of it.​
2. The child will have Sundays off from vacuuming, and yardwork, but will still do dishes.
3. The child will only be paid for the first 8 weeks, 6 days a week, Monday through Saturday.  The rest of the year's labor is completely free.
4. The child's payment for the first day will be one penny.  (Yes, just one cent.)
5. The second day's payment will be doubled to two pennies.
6. The third day's payment will be doubled again to four pennies.
7. Payment will continue doubling at this rate for the remainder of the 8 weeks (Sundays excluded).

Should you accept the Proposal?

Answer: Absolutely NOT!!!

Some reasonably intelligent folks have answered this question by saying, "Well, maybe if you were a millionaire, and had plenty to spare."

Nope.  Those folks are underestimating the power of exponents.  It wouldn't matter if you were the richest person on earth.  In fact, it wouldn't matter if you were as wealthy as the top 50 richest people in the world..... combined.

Why?

Because your total bill at the end of the 8 weeks would be more than $2.8 trillion!!!!  To be precise, the actual bill would be $2,814,749,767,106.55. (Mind you, don't forget the 55 cents - wouldn't want to cheat the poor kid, would you?)

Pretty hefty allowance, eh?

That's the power of exponents.  After the first week, you'd be feeling good, thinking you'd made a sweetheart deal.  Actually, you might even feel a bit guilty about taking advantage of your kid.  The first week's total payment would be the grand sum of 63 cents.

But then, at the end of the second week, some question marks might be popping up in your head.  After all, the second week's payment would be $40.32.  Seems a bit steep for an allowance.  And the worst part is, the first day of the third week will earn a paycheck of $40.96.  That's just the first day!  See, the paycheck for each day is actually one penny more than all the previous paychecks combined.

Now do you understand the power of exponents?

Okay, so if you understand exponents, how should you counter your kid's payment proposal?  I mean, you'd love the extra help around the house, and you'd like to instill appreciation in your child for a well-earned paycheck.  But I think you'd agree that $3 trillion is a bit excessive.

Well, one possibility is to answer this way:
"Johnny (or Jane), I really appreciate your offer, but I'd hate to work you too hard at your age.  You know, 'all work and no play' and all that.  So let's keep all of your conditions, except one.  I want you to have five Sundays a week, and the vacuuming and outside work (and the paychecks) will only be two days a week."

Will that be enough to save your financial solvency?  Well, the total bill now comes to $655.35.  That's a fair amount of money.  But remember, the dishes will be done every day for a year.  Vacuuming twice a week.  Yard work twice a week (and if you have a big yard, think how much a landscaping service would charge).  And don't forget the gardening!  Still think it's too steep?  Then grow a larger garden, and the kid can pay his own salary with the surplus vegetables.

Now, if you really want to skin your kid (as punishment for trying to skin you), you can take it one step further.  Allow vacuuming and yard work (and paychecks) on only one day a week.  That should be enough to get the weekly mowing and weedeating done.  Also, you'll get the vacuuming for that day, and maybe a little gardening.  Plus, don't forget you'll have all the dishes washed every day of the year.  

And how much would that set you back?

Ha!  A grand total of two dollars and fifty-five cents..... for the entire year!!!  Now that's a sweetheart deal!!

Ah, the power of exponents.