gpt-5.6-luna-pro × math

A SaaS product has 1,000 users.

• 60% use the free plan.
• Of free-plan users, 8% convert to paid each month.
• Paid users have a 4% monthly churn rate.
• No new users join.
• Conversion happens before churn each month.
• A converted user cannot churn during the same month they convert.

Question: After one month, how many free users and paid users are expected to remain?

Show the calculation clearly. Do not round intermediate values.

Output format: { "free_users_after_month_1": number, "paid_users_after_month_1": number, "calculation": ["...", "...", "..."], "assumptions": ["..."] }