In the Philippines, where we try to love, honor, and respect our elders, senior citizens are given a 20% discount on most goods and services.
Expanded Value Added Tax is a 12% tax on consumers which simply means that aside from being taxed for earning money, we also get taxed for spending it.
Anyway, to avoid confusing easily disgruntled customers, it was eventually mandated that the actual selling price (ASP), the price with e-VAT, be displayed on shops instead of the base selling price (BSP), the price without e-VAT. This makes more sense--less mental math for the budget conscious.
ASP = Base Selling Price plus e-VAT
ASP = ( 100% of BSP ) + ( 12% of BSP )
ASP = ( 100% + 12% ) of BSP
ASP = 112% of BSP
Prior to e-VAT exemption, senior citizens were only getting a net discount of 8%.
oldSCDP = Actual Selling Price minus senior citizens' discount
oldSCDP = ( 112% of BSP ) - ( 20% of BSP )
oldSCDP = ( 112% - 20% ) of BSP
oldSCDP = 92% of BSP
Fortunately, senior citizens are no longer burdened with e-VAT, allowing them to fully enjoy their 20% discount!
newSCDP = BSP minus senior citizen's discount
newSCDP = ( 100% of BSP ) - ( 20% of BSP )
newSCDP = ( 100% - 20% ) of BSP
newSCDP = 80% of BSP
However, the display price, the actual selling price (ASP), normally would already have e-VAT incorporated.
ASP = 1.12 x BSP
1.12 x BSP = ASP
BSP x 1.12 = ASP
BSP = ASP / 1.12
Note that multiplying the actual selling price by 0.88 is a "wrong cut", not a shortcut. We divide the actual selling price by 1.12 to get the base selling price.
newSCDP = 0.8 x BSP
newSCDP = 0.8 x ( ASP / 1.12 )
newSCDP = 0.714285714 x ASP
That last line suddenly makes it seem overly complicated. Not inherently obvious, but that's actually just a five over seven decimal fraction.
5 / 7 = 0.714285714
newSCDP = ASP x 5 / 7
To summarize, to get the senior citizen's discounted price from an e-VAT inclusive display price, multiply by five, then divide by seven. That's four fewer keytaps on the calculator.
