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Spare change is about $10 per pound

04 Mar

One red centAll of our household change goes into a big glass. It takes years to fill this glass at our current rate of coin accumulation. When it finally fills, I usually empty it into a CoinStar machine in exchange for an equal-value Amazon gift certificate (this is a great alternative to rolling coins for the bank). I enjoy the suspense when I go to the store because I have no idea how much they are actually worth. Of course, the CoinStar machine could be cheating me and I’d never know it! As a naturally suspicious person, this won’t do. When the glass filled up this month, I was determined to estimate the value myself first. Plus, it would be a great problem-solving exercise!

Yes, this is how I entertain myself. Thank you for asking.

The simplest way to tackle the problem could be by weight. I weighed myself on my bathroom scale with the full glass in my hand and then weighed myself again with the empty glass in hand. It appears that I have 6.4 pounds of American coinage. How much could that be worth?

I assumed this would be a fairly simple exercise. The standard masses of U.S. coins are readily available. By these figures, quarters and dimes are each worth $20 per pound, while nickels are worth $4.54 per pound and pennies a mere $1.46-$1.81 per pound depending on the mint year (the standard mass of the penny changed in 1982 when the mint replaced most of the copper in new pennies with zinc). That gives us a top and bottom estimate: Change is worth between $1.46 and $20 per pound, depending on the mix of coins.

I needed extra assumptions to refine the estimate for my situation. Here are the scenarios I tried:

  • If the change results from cash purchases, and any given cent value (0-99) is equally likely, and the cashier gives you the most efficient possible change, then typical change from purchases is worth $12.11 per pound.
  • Some people use all of their quarters for laundry or parking. Also, if your coins are scavenged from the street, there will be few quarters; people don’t lose large, valuable coins as readily as smaller, less valuable ones. Typical change without quarters is worth $5.42 per pound.
  • Prices are not actually random; many of them end with 9, resulting in extra pennies that reduce your change’s value per pound. Typical change from purchases ending in “9″ is worth $9.68 per pound. However, this rule assumes that you purchase only one item at a time and do not pay sales tax.
  • Overall, most mixed change is worth at least $9 per pound.

Coin jar

For my personal change, I assumed arbitrarily that I have would have 50% fewer quarters than chance alone would dictate, and I did not adjust for pricing gimmicks or sales tax. This gave me a value of $9.76 per pound. At that rate, my 6.4 pounds of change would be worth $62.48.

Off to the CoinStar to test the results!

Coinstar receipt

Apparently, I had more quarters and dimes than expected: my change was actually worth $69.18 or $10.81 per pound. That’s about 11% higher than my original estimate, but I won’t complain about having more money than I expected. I would rather be pleasantly surprised by a high value than be disappointed by a low one. Presumably, I am finding and keeping more quarters than I assumed.

I also know my bathroom scale is not perfect. Based on my tests, it has about 10% error on small increments of weight, so I don’t expect exact results. These are within a 10% margin of error by my figures.

These tests have given me a simple rule: When the coin jar fills up, assume it is worth $10 a pound.

The question: How much is spare change worth?

The answer: Usually $9-12 per pound — I would assume $10 per pound.

 
 

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  1. carbar

    03/30/2012 at 4:06 pm

    This is all well and good. But you seem to have forgotten the necessary last step: how many Special Brews can you buy with 6.4 lbs of change?