Gérard Lochon wrote:
You have a net value, 2 decimals provided, then
you calculate the taxes round(rate*net,2),
and then you add the net and the taxes to get the gross.
And the result can be different from round(net*(1+rate),2).
The true gross is always an addition (net+taxes), and
never a multiplication basis, this avoiding rounding deltas.
Going with the 21% VAT thought I'd test this out so knocked up a quick
program (below) to go up from 0.01 until you get a difference in the
calculation. You must go up to 18586.50 where the VAT is 3903.17
giving total of 22489.67 whereas the other method gives 22489.66
A bit more checking and the 0.01 error is also due to rounding errors.
When nNum is 18586.5 in the program below
nNum = 18586.499999958650
nVat = 3903.170000000000
nGross = 22489.669999958650
nMulti = 22489.660000000000 - This only comes out at this value because
nNum is below the exact value it should be. If you put into a calculator:
18586.5 * 1.21 = 22489.665 which should round up to 22489.67
In the program below if you put in
nNum = round(nNum,2) at the start of the loop you get no differences
up to 200,000. I'm sure if you go higher you will find some.
Think it's time to check a few programs ;-)
Peter
CLEAR
nNum = 0.01
nRate = 0.21
DO WHILE nNum < 100000
nVat = ROUND(nNum*nRate,2)
nGross = nNum + nVat
nMulti = ROUND(nNum*(1+nRate),2)
IF nGross <> nMulti
? 'Value ' + STR(nNum,9,2) + ' differs. ' + STR(nGross,10,2) +
STR(nMulti,10,2)
ENDIF
nNum = nNum + 0.01
ENDDO
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