December 29, 2011

Its OK to Round to the Dollar When Budgeting

Sometimes you'll see people talking about tracking your spending "to the penny" when discussing budgeting.   I don't know for sure if that is meant to be taken literally or not.   However I can confidently say that its not really necessary to track every cent of your spending.    It is OK to track your spending to the nearest dollar.   After you add it all up, rounding off the value of your purchases and expenses will be just about equivalent to tracking the exact numbers.

Lets look at an example of 10 figures.   Below are ten actual dollar value purchases from one of my credit card statements.  I compare the actual bill to the amounts rounded to the nearest dollar.

actual rounded
 $88.35  $88
 $35.00  $35
 $43.15  $43
 $95.32  $95
 $92.33  $92
 $28.89  $29
 $22.97  $23
 $60.00  $60
 $3.99  $4
 $42.27  $42
sum sum
 $512.27  $511.00

As you can see after you add up the totals the difference is only $1.27 out of $512.27.

If you have 10 transactions then the most that those could be off by rounding to the nearest dollar is $5.

For example lets say you had 10 purchases all of $1.50   If you rounded those to the nearest dollar you'd round up to $2.   That would mean you add 50¢ for each transaction and you'd be off by $5 total compared to the actual purchases.    However the cents values of your purchases are almost always going to be randomly distributed more than not.   You won't have a ton of purchases with 50¢ in change.  You'll have several purchases of 90¢ or more and many of 10¢ or less worth of change.   They will tend to even out over a larger sample.

I looked at a set of almost 500 purchases in my credit card statements to date.   For various groups of numbers I compared rounding to actual figures.

Looking at groups of 30 purchases the most that the rounded figures were off versus the actual numbers in total was $2.54     For groups of 10 purchases the sum of the rounded values was at worst $1.78 less than the sum of the actual numbers.  With a larger group of 60 figures the impact of rounding versus actual was $3.52 in worst case.   

As a percentage basis the error induced by rounding was usually around 0.1% to 0.2%.    The worst case I found was off by 0.5%.

If you're doing a monthly budget then you may have 20 to 30 individual financial transactions to record.   If you round those figures then its likely the rounding will only change the totals by a couple dollars which will be less than 0.5% difference.  

Bottom Line : Rounding off your spending transactions to the dollar is not going to change your budget in a meaningful way.   Rounding can save you some time and make budgeting easier.


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