[josephcsible]

Think of two scenarios where you're buying something for $1000.

Scenario 1: You use a credit card with a 2% cash back reward to make the purchase. You immediately pay off the credit card balance and claim the $20 of rewards. Your net cash flow is -$980 at time 0.

Scenario 2: You buy a 3-month zero-coupon CD for $980 today, and then use 3-month BNPL to make the purchase. In three months, the CD earns $20 of interest. You cash in the CD for $1000 and then use that $1000 to pay off the BNPL. Your net cash flow is again just -$980 at time 0.

The annual effective interest rate yielded by the CD for scenario 2 to work out exactly as described is roughly 8% (actually around 8.42%).

[RC_ITR]

Yes but who is going to pay you the 2% for the remaining 9 months?!?!

You’re incorporating a theoretical (and unrelated to 2% credit card rewards) interest rate into your calculations. I could easily say a CD yields 10% and this is a 50% APR then.

EDIT: Maybe to help you think about this: this is a purchase loan. It is not a cash loan. You got $1k worth of goods for $1k dollars. You can make arguments about opportunity costs, but that’s different than the traditional concept of APR.

EDIT 2: I’m posting banned but indulge me, what’s the APR of cash purchases?

[josephcsible]

> Yes but who is going to pay you the 2% for the remaining 9 months?!?!

Don't think of equalizing the terms by extending the BNPL. Think of equalizing the terms by shortening the CD.

> You’re incorporating a theoretical (and unrelated to 2% credit card rewards) interest rate into your calculations. I could easily say a CD yields 10% and this is a 50% APR then.

I'm not claiming that the ~8% interest rate is real. My calculations mean that if you can get that rate or better, then you should use 3-month BNPL, and if you can't, then you should use your credit card with 2% cash back instead.

> EDIT: Maybe to help you think about this: this is a purchase loan. It is not a cash loan. You got $1k worth of goods for $1k dollars. You can make arguments about opportunity costs, but that’s different than the traditional concept of APR.

I fail to see how that makes any difference.

> what’s the APR of cash purchases?

It's either the highest APR of any of your debt, if you have any, or the risk-free APR you could get from a savings account otherwise.

[RC_ITR]

> It's either the highest APR of any of your debt,

Yes, by your logic it is literally an infinite APR. $200 numerator / 0 years denominator. Doesn’t that imply that maybe your formula has some holes in it and this is a fundamentally different transaction (a take rate rather than an interest rate) than what you’re characterizing it as?

[josephcsible]

That equation is definitely wrong, but it's not the one that I've used anywhere.

[RC_ITR]

In your scenarios, your cash flow is -$1000 at time 0 if you pay with cash.

[josephcsible]

Okay, I think I see where you're coming from now. With the 2% reward from the credit card, using it today is -$980 today, and cash is -$1000 today. If you do the math to see what interest rate you'd need for paying cash to be the better option, you do indeed get an infinite APR. This matches with common sense: if your net cash flow is zero at all future times either way, you're always better off paying $980 today rather than $1000, no matter what interest rates are.