Leasing a BMW i3, cheapest option, in CPH will cost you 211870 DKR for 36 months, or 31636.55 USD. This comes to about 0.136 DKR/minute, vs 3.50 DKR/minute for the rental.
The difference is 25.7 times, or, for every 25.7 minute you have the lease car, you can drive the above solution for 1 minute, or, 6.5 hours of driving per week.
If you only need it for odd trips once or twice a week, which, since you're living in a modern city (CPH) is more than likely, the 3.50 DKR/minute is miles cheaper than a lease-option, and still significantly cheaper than buying, insuring, fueling, and maintaining a BMW i3, even if we only look at direct costs, and ignore financing and time spent cleaning and maintaining a leased or bought car.
Note: I didn't see a new-price for a BMW i3 on the BMW website, but a used-car dealer's cheapest option is a 2014 model for 299.885 DKR