What should I be thinking about when considering the annual discount? Is there a 'right' number that I should be targeting?
So far, I've considered that the fees I pay are lower for annual customers, and the risk of mid-year churn is somewhat lower. Are there other relevant considerations?
I understand why new customers would sign up for a monthly plan, to try it out (there's also a 2-week free trial, before having to pay). Should I be contacting customers who are still with me after a couple months and encouraging them to switch to annual subscriptions? Or should I not really care?
At a high level, you need decide whether you have figured out a product market fit, calculate CAC (customer acquisition cost), Churn rate for monthly vs annual.
If you are still testing your product and are not sure whether you have a fit then I would recommend continue with monthly plan and don't worry about annual plan. You will learn plenty about your product (based on Churn) from monthly subscribers.
If you are past the product market fit stage, annual plan provides you the best option. a) Average CAC is lower b) Churn is lower c) Most importantly, you generate cashflow by getting more money upfront.
There is also the hybrid option you can try, which is annual contract with monthly payments.
a. Finding additional markets of customers
b. Making your product more appealing to increase your conversion rate
c. Maybe switching payment processors to one with lower fees and a lower churn rate