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One thing is with Sharia they forbid the paying of interest. Wonder how that will work.

It's simple. They just relabel the interest (riba) as rent. Example:

Declining Balance Co-ownership Program
Guidance Residential is the #1 U.S. provider of Shariah-compliant home financing. Our Declining Balance Co-ownership Program is modeled on the Islamic concept of ‘Musharakah Mutanaqisa’ or diminishing partnership. The program has been certified by an independent Shariah Supervisory Board, which performs an annual audit to ensure absolute compliance with Shariah.
In this model, Guidance Residential and the homebuyer engage in a joint ownership venture where each owns a percentage of the home equal to the equity they each contributed. Homebuyers are required to make monthly payments to Guidance Residential over a predetermined period of time in order to completely buy out Guidance Residential’s equity, and own the property outright. The monthly payment consists of two portions; an amount that is allocated for acquisition of Guidance Residential’s equity and the other allocated as rent for use of the portion of the home they do not yet own. The acquisition amount helps in buying Guidance Residential’s shares of ownership over the predetermined period of time and the rent is the profit Guidance Residential earns from this co-ownership program.