Email discounts on already discounted plans

Hi guys!

I got into a discussion around pricing with my co-founder, and we seem to disagree quite a lot. First I want to give you a little bit of a background info:

We currently have an email funnel which the user enters as soon as they sign up as a trial user, this has produced great results for us in the past. At the end of the trial period, one of the emails contain an offer of 10% in the form of a Stripe coupon code which they can use on either a monthly subscription or a yearly subscription (only on the first year).

The yearly subscription is (already) discounted by ~20% to "give" our customers incentive to go for that instead of the monthly subscription.

So the question is:

Should we discount the (already) discounted yearly plan by another 10% in the email flow to nudge our users? Or change the wording in the email to indicate that by choosing the yearly plan, they already get ~20% discount.

Really looking forward to hear your input on this one!