## Finance: buy-now-pay-later in the time of inflation

23 April 2022

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.

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:

• $\frac13 \times (\frac{1}{1.08}) ^ {0.5/12}$
• $\frac13 \times (\frac{1}{1.08}) ^ {1.5/12}$
• $\frac13 \times (\frac{1}{1.08}) ^ {2.5/12}$