Supermarket savings

I recently got a loyalty card for my local supermarket. As a reward, they sent me some vouchers off either shopping or petrol (on alternate weeks) if I spent £20 per week over 4 consecutive weeks. If I spent all 4 vouchers, there would even be some bonus points.

Having used some of these vouchers, they then sent me some more vouchers if I spent £30 per week over the next 6 weeks. This felt like a very sneaky way to get me to spend more money. Were they trying to get more money out of me? Would spending more money actually result in bigger savings? I decided to try and find out…

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Preliminary calculations

I first looked at my current average spend. This turns out to be approx. £25 per shop. So far so good, however my average length of time between shops is 10 days. Obviously this doesn’t fit well into a voucher system which requires usage on a 7-day visit system. Converting my average spend to a 7 day shop gives an average spend of £18.

Before we continue, I should list some assumptions I have made in the following calculations:

1. Every week’s shop is exactly the amount of the average spend. [In reality, some weeks would be higher and some would be lower.]
2. The most savings on fuel would be for filling the car from empty. At a 45litre capacity and 6p off per litre, this gives a saving of £2.70. [In reality it’s very rare that I would need this much fuel, especially not every 2 weeks.]
3. A 10-day shop cycle can be converted to a 7-day shop cycle. [In reality this doesn’t work due to volume purchasing, expiry dates, etc.]
4. The extra reward points gained from spending more money is negligible in calculating savings.
5. The additional fuel cost of going to the supermarket every 7 days compared to every 10 days is negligible.

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£20 voucher set

Scenario 1 : Spend of £20 every 7 days (Compared to £18 spend every 7 days)
[table id=1 /]

Scenario 2 : Spend of £25 every 10 days (Starting on Day 2 to maximise savings)
[table id=2 /]

Conclusion: Surprisingly, I would actually save money by going shopping less often and spending more each time.

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£30 voucher set

Scenario 3 : Spend of £30 every 7 days (Compared to £18 spend every 7 days)
[table id=3 /]

Scenario 4 : Spend of £30 every 10 days (Starting on day 1, Compared to £25 spend every 10 days)
[table id=4 /]

Scenario 5 : Spend of £25 every 10 days (Starting on day 1)
[table id=5 /]

Conclusion: None of these vouchers would save me money. In fact, I could end up spending far more than I saved. By not spending enough for any voucher, I don’t save anything, but I also don’t lose anything.

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So there you have it, initial savings followed by a large increase in spending. I certainly won’t go out of my way to meet the spending targets anyway. What do you think? Have I missed something? Have I made any mathematical mistakes?

In reality, all of these scenarios are impossible. This entire article is hypothetical as I’ve not been to the supermarket for the last two weeks due to a dodgy tub of tuna.