The others are right, There are no ways of getting a truly accurate measure other than just counting the coins. The missing factor is someone’s spending patterns. Other people got the ratios of average coins stored correct assuming it is truly random but it hardly ever is. It depends on what you buy and what you put in the jar. I spend quarters freely for example but I throw pennies, nickles and dimes into my coin jar. Quarters are the highest value common coin so how you treat those can greatly influence the total value of the jar.
The best way to approach this problem is through statistical trials of similar circumstances. A given person with the same coin jar will end up with very similar value for a given volume of coins. It will also be extremely similar to other people with the same habits.
I can tell you what the result will be within reason for a pickle jar that size because I have done it before myself. It is between $200 and $300 like other people said. My pick is $283.16. Go to a Coinstar machine and check it and post the results. Pro-tips: Most of them offer gift cards from major retailers so it doesn’t cost you anything if you have a place to spend it. Rolling coins to take to the bank is a fool’s errand. Also, lift the sorting tray up with your fingers so that it is at a downward angle the whole time and then just scrape the coins in with your fingers. Many people don’t do it correctly and it takes 5x longer than necessary.
Well, actually, I think our spread is much higher than that. I said $150-$200 for the half-filled gallon jar, based on $300-$400 per gallon of mixed change. Leo Bloom’s site that 39 oz of roast coffee beans would equal .67 gallons and Hail Ant’s reporting that such a filled container returned $350 would put it at $522 per gallon (!), which seems high to me.
This guy got $2212.30 out of a filled-to-the-brim 5 gallon jar, for $442.46 per gallon. Now, my hunch is that is not going to downscale perfectly, and you’re going to get a good bit less per gallon with a one gallon jar, but that should leave you in the $300-$400 per gallon range.
That said, as you said, it depends on your spending habits and what change you save. I tend to pick quarters out of the change pile or my pocket, so that would influence the count. If the OP really does have an equal distribution, I could believe the higher end of the estimate.
As I understand it, most banks no longer want human-rolled coins. Too many people try to use them for fraud. So don’t waste your time rolling your own. Just bring them in loose and let them run them through their machine. My bank, in fact, has a self-serve coin counting machine in the lobby. I just put all my loose change into it and it gives me back a receipt that I take to the teller to deposit. And I don’t have to pay anyone 9% for this service.
However, I rarely use this machine. Nowadays, I usually get rid of my coins by spending them. But then I buy lots fo stuff with cash that most people use credit cards for, such as groceries and gasoline. I try to (and usually succeed in) paying exact change in these transactions.
But I do have a jar of coins, well two of them. But the coins in them don’t come from my change, but rather a different source. I bicycle a lot, and about 10 years ago started noticing a lot of coins on the side of the roads. For reasons I can’t quite explain, I started to pick them up and put them in jars. I only put found coins in these jars, never change from transactions. One jar is full, the other is about 75% full. They’re one-quart mayonaise jars, although the full one is packed to the brim, so it’s closer to a liter of coins.
Some day I’ll probably take them to the bank to have them counted. I expect numerous rejects by the machine, though, especially the pennies. You see, it doesn’t take too many times being run over before pennies lose most of their copper coating. I assume the machines go by the electrical properties of the coins and roadkilled pennies will not have the same properties as ordinary ones.
Well, if I ever do cash them in, I’ll have a guess-the-total contest in the Game Room or somewhere. But I’m in no hurry to do that.
If each coin is an integral multiple of the smaller coins, it would be easy. For example, if no dimes were used then average change would be 1.5 quarters, 2 nickels and 2 pennies. (These sum to $0.495 as expected.) With K pieces of a quadloon, (K-1)/2 is the expected number of pieces; there are K=4 quarters in a dollar, so (4-1)/2 = 1.5 is expected, and so on.
Multiply these numbers by 100 to get (except for the dimes and nickels) the numbers Chronos posted:
150 : 0 : 200 : 200
Quarters do not have a whole number of dimes, so allowing dimes complicates. Simplest is to just write a table showing how the five equally probable cases of nickels change into nickels and dimes:
0 1 2 3 4 – nickels only, average 2
0 1 0 1 0 – nickels, average 0.4
0 0 1 1 2 – dimes, average 0.8
Net result
150 : 80 : 40 : 200
Even with the dime “problem”, a “greedy” algorithm leads to a minimal number of coins in the U.S., but this isn’t generally true. For example, suppose a 7-cent septam were provided instead of 10-cent dime. To provide 11 cents change, a greedy algorithm would give five coins (1 septam, 4 pennies), when only three are needed (2 nickels, 1 penny).
Protip: self-checkout machines take change just fine. Use your quarters and even dimes at full value.
Use coinstar or similar for pennies and nickels when the jar gets too full.
Also, a hundred pennies weighs a pound, to help answer the OP.
Exactly. I take my coins to the local CVS and their Coinstar machine. There’s no way I’m NOT going to spend several hundred dollars at the CVS in the next few months, so a “gift card” there is as good as cash to me.
Regarding Coinstar machines: The one I use lists several options for gift certificates. I pick Amazon. (Which of course gets used fairly quickly.) No surcharge. I assume Coinstar makes it’s money off of unused gift certificates plus a little bit of kickback from the gift certificate retailer per purchase.
Back when I worked for a convenience store, there were a few times when we ran short of pennies (region-wide shortages). In those cases we encouraged customers to bring their pennies in. The easiest way to cash them in was to weigh them on our produce scale… to do this we had to calculate the per pound price of pennies, which we did by plopping them down on the scale until the weight read “1.00”. It took 144 pennies to make a pound. Obviously this could go up or down a few, but I’m pretty sure that 100 pennies is going to come up well short of a pound.
Actually, I have a postal scale, if I have time later I’ll post the per pound price of all the common coins.
it turns out that quarters and dimes both have the same dollar/pound value, and that’s about $20/lb - i’m saving just those two in a five gallon water (plastic!!) bottle… it’s been a long haul, but it’s maybe 2/3 full and weighs over 100 pounds. that’s some serious change
I do the coffee can thing, fill it to the brim, and it’s remarkable how close it comes to $105 every time. I’ve won prizes from the Coinstar machine for guessing the total value within a certain range. I always guess $105. Last time I was only 16 cents off, which amazed the teller.
I once had a water-cooler jar full of miscellaneous change to deal with.
I found it interesting that dimes and quarters are worth the same amount per unit weight. I forget the coefficient, but it should be easy to look up. Something very simple like $10/lb, IIRC.
The value of pennies and nickels per unit weight is tiny in comparison (IIRC, under 10% of the total in my case).
So, if you can measure the percentage of quarters and dimes by weight in a representative sample and extrapolate to the full weight, that should get you in the ballpark.