Final answer:
The unearned revenue at year-end on December 31 for the new gym is calculated by considering the memberships that have been paid for but not yet fully provided. The total unearned revenue from the 32 members (12 in November and 20 in December) is $4,880.
Step-by-step explanation:
To calculate the unearned revenue at year-end on December 31 for the new gym, we need to account for the membership fees that have been collected in advance but for which the service has not yet been provided. The gym charges an annual membership of $240. In November, 12 people signed up starting December 1, and in December, an additional 20 people signed up starting December 15.
For the 12 members who signed up in November, the entire month of December is unearned, as none of their service period has elapsed by December 31. Therefore, the unearned revenue from November sign-ups is 12 members × $240/year = $2,880.
For the December sign-ups, only half of December is unearned as their membership starts mid-month on December 15. So, the calculation for their unearned revenue is (20 members × $240/year) × (1/2 month / 12 months) = $2,000.
Adding both amounts gives us the total unearned revenue on December 31, which is $2,880 (from November) + $2,000 (from December) = $4,880.