Product Pricing & fractional pennies

So I have a product where the price is is determined by multiplying a base price by a factor that increases by age. So depending on how old someone is when they buy the product the price is different. The factors are out to the 3rd decimal place. (Yes this is the insurance industry). Perhaps this question belongs in different forum my apologies if this is the case.

Example 1: Individual buys 1 plan Base Price is 187.39 factor is 1.087. Everyone agrees consumer pays \$203.69 even though the price to the third decimal place is now \$203.693. We sensibly round down/truncate here.

Example 2: Individual buys plan for entire family.

a. Subscriber Base price is 187.39, factor is 1.087. Total price rounded =203.69, and rounded to 3rd decimal place is 203.693

b. Dependent 1. base Price is the same, factor is 1.048. The unrounded price is 196.385. Truncated/rounded down is 196.38.

c. Dependent 2. base Price is the same, factor is 0.765. unrounded price is 143.353. The rounded price is 143.35.

The crux of the issue is that according to the almighty excel spreadsheet that everyone except me believes, suddenly the same customer owes the fractional pennies because the sums of the fractional pennies add to a cent. But we truncated/rounded in the prior example. Its not consistent. It is my belief we should be rounding down to 2 decimal places every time we multiply. According to others at work currency should be handled to 3 decimal places.

My counter example was that if multiplication were involved in the pricing of any commodity, pants at the store for example, and I just got pants for myself I don't pay any fractional cents, but suddenly when I buy multiple pants for my kids, I owe an extra cent. Its not like stores display numbers beyond the 2nd decimal place. If I look at my receipt and add the numbers up, it should make...cents ha ha.

I guess another way to phrase the question would be: Are fractional pennies something that can be written off for tax purposes as a loss, or is it just imaginary money like I believe it to be that should be rounded down/truncated?

I guess I could see the argument going the other way if currency is to be handled to the 3rd decimal place like some folks (such as the cast of The Office) allege.

TL;DR In general, is currency handled to the third decimal place?

• Rounding should always occur as the final step of a calculation, not during intermediate steps. Otherwise rounding errors accumulate given the number of steps in a particular calculation. This is common practice in many industries, and if you want a customer-facing example, in Canada the literal metal penny has been eliminated. When you buy something for \$1.04, you actually pay \$1.05. When you buy something for \$1.02, you actually pay \$1.00. BUT if you pay by credit card, or electronic means, you would still pay the exact amount. That aside, this is not really a personal finance question. – Grade 'Eh' Bacon Jan 9 '18 at 17:49
• @Grade'Eh'Bacon re:Canada I detest the penny and long for the day that the US establishes a similar policy. – D Stanley Jan 9 '18 at 17:58
• If buy pants from a store in a jurisdiction that levies sales tax, you can end up owing extra pennies when buy products together versus separate, exactly like your insurance example due to rounding of the tax on the total. – Shannon Severance Jan 9 '18 at 18:19
• @user3042053 Your real issue does seem to be how to handle confrontation at work - the underlying question relies on whether you are 'right', but whether 'right' or 'wrong', there is a communication problem at your office where you don't feel comfortable expressing these comments (or, perhaps you are a little on the novice side of things, and aren't accepting proper feedback from your manager/coworkers). – Grade 'Eh' Bacon Jan 9 '18 at 20:11
• At a former employer, I had many long arguments initiated by a junior accountant that the system I supported was working correctly on a daily Work In Process report "Machine count x list price" value did not match the "Job percent completion x quoted price" value by up to several pennies, because of a variant on this. We eventually reached a detente that I would only look into the system if the amount was off by a dollar or more. On the other hand, see Richard Pryor's character in Superman III. – user662852 Jan 9 '18 at 20:13

There is no law that requires that all prices be rounded to the nearest penny. Have you noticed that virtually every gas station in the US includes 0.9 cents per gallon in their gas prices? The price is not rounded until the total price is computed by multiplying by the amount.

So if the companies pricing policy is to only round the total after computing the prices for all individuals (including fractional cents) there's no general law to prevent that. There may be regulations in the insurance industry that could influence the policy, but nothing inherent to the currency or pricing policy overall.

• Yes gas prices at fractional pennies is the gold-standard example of this practice - listed right there on the billboard! – Grade 'Eh' Bacon Jan 9 '18 at 18:02
• But gas prices are a bad example. You don't keep track of all your gas purchases for the month, add them together and then pay the service station. – mhoran_psprep Jan 9 '18 at 19:10
• @mhoran_psprep Imagine gas costs \$1.001 / gallon. If you buy 1 gallon of gas, you pay \$1. If you buy 1 gallon 10 separate times, you pay \$10. If you buy 10 gallons at once, you pay 10 * 1.001 = \$10.01. Note that paying separately, you get to 'round down' each transaction, but buying 10 gallons at once, 'rounds up' to an extra penny. – Grade 'Eh' Bacon Jan 9 '18 at 20:14

In general, is currency handled to the third decimal place?

Not unless the currency has a 1/1000ths denomination (e.g. the old USA mil).

The currency should be handled as currency at all points where currency is actually involved. This means when the customer pays their bill, on the total amount you've agreed with them. How you calculate that price is up to you, though customers generally like to see a receipt that adds up.

Bear in mind that whenever you introduce rounding, at 3, 4, or 18 decimal places, you are going to hit edge cases where the rounded amount crosses a boundary between pennies that you weren't expecting, especially if you deal with non-integer multipliers, such as your age factor.

The cleverest solution I've seen is an old DOS-based point of sale system that calculated the total, then worked back through the calculation adjusting the line totals so that they appear to add up to the transaction total, and then adjusting the unit price on the line that was changed so it looks like that calculation was correct. As long as the rounding is always in the customers favour, this method produces the fewest complaints.