Insurance for rental property

[Jonathan Leblond]

Hi, I need help with different type of insurance. I think I heard on a podcast that you can insure only the value of the mortgage for a rental. For example, 

1. The building is bought for $200 000. 

2. The mortgage is $160 000

3. Reconstruction cost estimated by insurance cie $600 000

Can I get insurance for only $160 000 or $200 000 instead of $600 000? Or can I get something in between? The idea here is to save on insurance cost and if something happens we would just put the money in another deal instead of building it back. On a small scale it might not seam like a good idea but on a big picture a lot of insurance cost could be saved and the risk to lose everything is not that big. I tried to find info on BP but I don't remember on which podcast I heard something like that or where I read it. Insurance cie seems to say there is no other way to set the insurance than the $600 000 value.

Thanks