Regular updates will come later, but for now, i wanted to blog about something that i finally figured out. sometime earlier this year, i was doing some number-crunching on whether paying for petrol by credit card or using the straight up cash discount was cheaper. the thing that bugged me was that there were 3 variables for 2 equations, meaning that i couldn't solve for everything. but i managed to work it out and convince myself after graphing it on excel.

so it's pretty standard - total amount spent = price of petrol per litre X litres of petrol pumped. previously, i'd been doing it from an "amount spent" perspective, when i realized that i should be doing it from an "amount saved" perspective. the cash discount is straightforward, i save 2 yen per litre, so amount saved = 2 X litres of petrol. the credit card case is more convoluted. i get 1% of my amount spent back in points, and 1 point is the equivalent of 1 yen. in this case, amount saved = 0.01 X price of petrol per litre X litres of petrol.

plotting graphs of amount saved against litres of petrol, we get straight lines diverging from the origin, with gradients 2 and (0.01 X price of petrol per litre) for the cash and credit card cases respectively. so what this means is that for a given price of petrol, one will always win out regardless of volume. and the crossover point is when the gradients are equal, ie. 0.01 X price = 2. by some observation, we can see that as long as petrol price stays under 200 yen, it is always better for me to pay using cash. at 200 yen, both methods are equally good. above 200 yen, the discount from paying by credit card wins out.

this is of no serious consequence at all, and in fact may be an example of a new japanese word i picked up - 考えすぎ (overthinking), but i feel oddly satisfied/proud for having figured it out. also while doing research on this, i realized it seems that i can ask the cashier at family mart to scan the barcode on my card before paying with it to earn double points. considering that i've probably spent less than 5000 yen there, losing out on 50 points at max doesn't hurt too much. but now i know!

-random thought of the day: City trip next week, I think.-