Looking for financial answer, not opinion on down payment size

[Danny McGreevy]

I’m not interested in a personal situation answer, im interested in a pure numbers answer.  

I hope I can phrase this in a clear way.

Scenario: 

1) Is it better to avoid mortgage interest and put say 20% down or 

2) is it better to put down 10% to pay more mortgage interest if you can make the same returns on the money not put down? For argument sake, say that the mortgage interest rate is 10% and the returns of the money not put down are also 10% in the market

or is it the same result?

Don't consider PMI for this scenario

[Jack Seiden]

Quote from @Danny McGreevy:

I’m not interested in a personal situation answer, im interested in a pure numbers answer.  

I hope I can phrase this in a clear way.

Scenario: 

1) Is it better to avoid mortgage interest and put say 20% down or 

2) is it better to put down 10% to pay more mortgage interest if you can make the same returns on the money not put down? For argument sake, say that the mortgage interest rate is 10% and the returns of the money not put down are also 10% in the market

or is it the same result?

Don't consider PMI for this scenario

Number 1 is easily the answer in number two you break even, take on 10% debt to make 10% in the market, there's zero real return there, so may as well not pay pmi. Than the 2nd part is obviously there is no risk adjusted 10% return that exist's so in reality you are taking on guaranteed 10% debt for a on average lower return.