In a time of high inflation, if one can pay the same amount later it makes sense to do so, because inflation means that some quantity of money is worth less in the future.
Consider a common payment structure offered by one of the newish buy-now-pay-later companies, which offers a split payment without charging interest.
The below calculations are based on an offering from Klarna, a well-known buy-now-pay-later (BNPL) provider, which offers the below in the UK under the tag line 'Pay in 3'.
For a purchase of value 1, repayments are:
- $\frac 13$ at the time
- $\frac 13$ 1 month later
- $\frac 13$ 2 months later
Let’s assume that payments are made with a credit card where the balance is paid at the end of a given month. On average, spending will be in the middle of the month, and so we can assume the balance is on credit for half a month. We then have:
- $\frac 13$ 1/2 a month later
- $\frac 13$ after 1 1/2 months
- $\frac 13$ after 2 1/2 months
Assuming inflation at 8%, how much would we save?
Our discount rate is $(\frac{1}{1+r}) ^ {t/12}$ where $r$ is rate of inflation and $t$ is time period to in months, so the present value of our payments become:
- $\frac13 \times (\frac{1}{1.08}) ^ {0.5/12}$
- $\frac13 \times (\frac{1}{1.08}) ^ {1.5/12}$
- $\frac13 \times (\frac{1}{1.08}) ^ {2.5/12}$
Or, spreadsheet-style:
Payment | Timing (months) | Discount rate | Present value | |
---|---|---|---|---|
First payment | 33.3 | D+0.5 | 0.9968 | 33.2 |
Second payment | 33.3 | D+1.5 | 0.9904 | 33.0 |
Third payment | 33.3 | D+2.5 | 0.9841 | 32.8 |
Sum | 100 | 99.0 | ||
Implied discount | 1.0% |
Clearly, if at any point one pays interest this does not work. But if one can avoid that, it becomes a 1% discount on the price of consumer goods, and so it makes sense to do that if you can.
And so if the consumer can pay these charges without recourse to credit with interest, and they are rational, they will do this.