[RC_ITR]

> by using BNPL you forego 2% or whatever in credit card rewards, so you’re effectively paying ~8% annualized for a 3-month term.

I love your chutzpah, but you don’t get to do that math that way. The 2% doesn’t compound, it’s a one-time thing (unless you’re continually rolling over your BNPL purchases)

[tfehring]

It’s still useful to convert to an annualized interest rate even if your “investment” period is less than a year, because annualized returns are the standard unit of measurement for investment returns.

For example, if you’re debating whether to use a 2% rewards credit card or to use BNPL and keep the difference in a savings or money market account for 90 days, the latter strategy only wins if that account is yielding more than ~8%. Or if you’re deciding whether to use BNPL to let you pay down other debt a little faster, it’s only worth it if the interest rate on that debt is above ~8%.

[RC_ITR]

Yes. But let’s break this into first principles. You get $200 rewards on a $10k purchase. In no world do you get $800 on $10k. You only get $800 on $40k because the 2% isn’t a rate in principle so 8% literally never happens.

[tfehring]

The opportunity cost of 2% credit card rewards isn't a rate, but you can convert it to a rate by dividing by the time period. If you forego $200 in rewards to keep $10k for an extra 3 months, you're paying $67 or 0.67% per month for that money. If you instead forego that same $200 in rewards but get to keep your money for 6 months, you're only paying $33 or 0.33% per month. Converting those monthly rates to annualized rates of ~8% and ~4% respectively is just a matter of convenience, the math still works out the same if you keep everything on a monthly basis instead.

[RC_ITR]

But I’m telling you annualizing something like that is not convenience, it’s misleading.

Does every cash purchase also have an infinite APR? Because there I’m paying $200 for nothing. If that’s not logical then where does it start being logical?

[pandaman]

It's pretty simple really. Consider two scenarios of buying a $100 item:

a) pay with a 2% reward credit card

b) pay with BNPL scheme with a 3 month term.

In the scenario a) you effectively paid $98 right away and in the scenario b) you pay $100 but after 90 days (let's say you don't have monthly payments for simplicity). For b) to be no more expensive than a) you need a way to make at least $2 from a $100 investment in 90 days. This means that whatever investment you make with the $100 has to yield 8% annually. Even though you withdraw money after 90 days.

If you have monthly payments you need even higher yield to compete with the 2% reward. E.g. if you pay $33.33 every month then you need to make 1% yield per month to collect $2 off your initial $100 in 3 months: you get 3 months of yield from the final $33.33 payment, 2 months of the previous payment and 1 month of the first payment for total 6 months yield from $33.33. That's 12% annualized yield.

[RC_ITR]

You’re not answering my question about cash.

[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.

[tobyjsullivan]

Where did the parent suggest there was compounding? I read it as 2% of the purchase price, on a 3-month term. 2% * 4 = 8% annually, without compounding.

[RC_ITR]

Yes. But let’s break this into first principles.

You get $200 rewards on a $10k purchase.

In no world do you get $800 on $10k. You only get $800 on $40k because the 2% isn’t a rate in principle so 8% literally never happens.