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<p>[QUOTE="Troodon, post: 26545394, member: 4626"]It works out the same either way. I was making the assumption that they'll round <i>in favor of the customer</i>, not necessarily to the nearest nickel if the nearest nickel is in favor of the store, so if the change they need to give the customer is 1 cent, they'll give out 5 cents, thus costing them 4 cents. If they round down to 0, they cost the customer 1 cent... and that might lead to customer complaints or legal hassles (I don't know who's getting the law involved for 1 cent lol but you know, some bored lawyer with time on his hands might try a class action lawsuit or something).</p><p><br /></p><p>You're looking at it from the other end of the transaction: if the customer owes the store $1.01, the store will ask for $1.00, thus costing the store 1 cent. I was looking at it from the perspective of how much change is due to the customer, not the total the customer needs to pay to the store.</p><p><br /></p><p>But it's a distinction that makes no difference, because the math works out the same either way. Both ways are correct, and arrive at the same answer. The average cost of rounding to the nearest nickel, if always done in the customer's favor, and assuming all 10 digits have equal chances of coming up, is 2 cents per cash transaction.</p><p><br /></p><p>But... if they round to the nearest nickel always, even when it's in favor of the store... then the average cost per transaction (again assuming all digits have equal chances of showing up)...</p><p><br /></p><p>Change due if it ends in _ will cost them:</p><p>0 or 5: 0</p><p>1 or 6: -1 cent</p><p>2 or 7: -2 cents</p><p>3 or 8: 2 cents</p><p>4 or 9: 1 cent</p><p><br /></p><p>An average cost of... nothing. In theory that makes this method mutually beneficial. But I'm sure a store is willing to lose an average of 2 cents per cash transaction for the sake of customer goodwill, avoiding complaints, and avoiding legal hassle. That's less than it costs them to accept credit and debit cards.</p><p><br /></p><p>TLDR: Average cost of rounding to the nearest nickel (assuming all 10 terminal digits are equally likely) if always done in the customer's favor: 2 cents per cash transaction. Average cost of rounding to the nearest nickel, regardless of whether that favors the store or the customer (again assuming all 10 digits are equally likely): 0.[/QUOTE]</p><p><br /></p>
[QUOTE="Troodon, post: 26545394, member: 4626"]It works out the same either way. I was making the assumption that they'll round [I]in favor of the customer[/I], not necessarily to the nearest nickel if the nearest nickel is in favor of the store, so if the change they need to give the customer is 1 cent, they'll give out 5 cents, thus costing them 4 cents. If they round down to 0, they cost the customer 1 cent... and that might lead to customer complaints or legal hassles (I don't know who's getting the law involved for 1 cent lol but you know, some bored lawyer with time on his hands might try a class action lawsuit or something). You're looking at it from the other end of the transaction: if the customer owes the store $1.01, the store will ask for $1.00, thus costing the store 1 cent. I was looking at it from the perspective of how much change is due to the customer, not the total the customer needs to pay to the store. But it's a distinction that makes no difference, because the math works out the same either way. Both ways are correct, and arrive at the same answer. The average cost of rounding to the nearest nickel, if always done in the customer's favor, and assuming all 10 digits have equal chances of coming up, is 2 cents per cash transaction. But... if they round to the nearest nickel always, even when it's in favor of the store... then the average cost per transaction (again assuming all digits have equal chances of showing up)... Change due if it ends in _ will cost them: 0 or 5: 0 1 or 6: -1 cent 2 or 7: -2 cents 3 or 8: 2 cents 4 or 9: 1 cent An average cost of... nothing. In theory that makes this method mutually beneficial. But I'm sure a store is willing to lose an average of 2 cents per cash transaction for the sake of customer goodwill, avoiding complaints, and avoiding legal hassle. That's less than it costs them to accept credit and debit cards. TLDR: Average cost of rounding to the nearest nickel (assuming all 10 terminal digits are equally likely) if always done in the customer's favor: 2 cents per cash transaction. Average cost of rounding to the nearest nickel, regardless of whether that favors the store or the customer (again assuming all 10 digits are equally likely): 0.[/QUOTE]
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