All 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: Read the rest of this entry »