It’s common for monthly subscription services to offer a discount if you pay annually instead. That might be a bad deal.

Example: Suppose a one-month subscription costs $10/month and one-year subscription gives you a 10% discount, which averages out to $9/month. Say you expect to maintain a subscription for about three years before canceling.

A one-year subscription will save you about $36 ($1 per month for 36 months), but you can also expect to waste $54: when you decide to stop using it, you will still have (on average) six months of subscription left ($54 = $9/month for 6 months). So you end up spending $18 more than you would have with the monthly plan.

If you get a one-year subscription that you expect to last three years, then you will end up wasting 1/6 of the total amount you paid for (in expectation). That’s only worth it if the annual subscription offers a discount greater than 1/6.

If you expect to use the service for five years, you need to get at least a 10% discount to justify switching to an annual subscription.

In general, you need to use the subscription for at least N years to justify a discount of 1/(2N).

How do you guess how long you’ll keep using the service? According to the Lindy effect, you should expect that you will maintain a subscription for as long again as you’ve already had it for. Therefore, if you can get a 10% discount with an annual plan and you’ve already had the subscription for more than five years, you should go ahead and buy the annual plan.