Amazon doesn’t always have the lowest prices on items, but they often do. One way to save on purchases that you regularly make is to subscribe and recieve them regularly from Amazon, with free shipping. They call this their Subscribe & Save service.
But here’s how to save extra money. If you subscribe to only one item, you get a 5% discount. But if you subscribe to 5 items, you save 15%. The question is:
Q: What is the maximum cost of other items I can add and still pay the same price when the 15% discount kicks in?
The answer is in this formula:
X <= .118S
where X = maximum amount you can add
and S = starting price you are already committed to ordering
This is what you get when you solve for X in this initial formula.
S – 0.05S >= S+X – .15(S+X)
So, for example, if you want to buy an item(s) for $30 using subscribe and save, the maximum cost of items you can add in order to get the 15% discount and pay no more is about $3.52.
Now, that is not really possible, but if the starting amount is more, say $40, the max amount you can add and pay the same total amount is $4.72.
Realistically, though, since few filler items are less than about $2, you would have to already be at 3 items for $40 to make this work. As you can see, the number of items you have to add and the starting price make a difference – in short, it’s hard to save money by trying to push to the 15% / 5-item level.
What about sales tax?
Well, the starting formula is a little more complex, but not bad.
TS + S -0.5S >= (S+X) – .15(S+X) + T(S+X)
As it turns out, sales tax doesn’t make that much difference in the calculation UNLESS you are buying a lot of stuff. I’ll spare you the algebra, but here’s the formula with sales tax added in. And no, there is no shipping cost, since these items ship free. Solving the equation:
X <= S / (8.5 + 10T)
where T = Tax (e.g. 9.25% tax, T = .0925)
So in the $40 example above, you could spend up to $4.65 here in California (9.25% tax), whereas the simple calculation gave you $4.72. So not much difference if you include sales taxes.
If you already have close to 5 items on Subscribe & Save, adding one or two low cost ($2 each) items will get you some more stuff free. Otherwise, you’re better sticking with the one item and 5% discount. QED.