Guidance Residential in Reston, Virginia, offers a Shari'ah-compliant housing finance product for Muslims and others who do not believe in collecting or paying interest. Under their Declining Balance Co-Ownership Program, Guidance will act as a co-purchaser who will act as a co-owner to the property and agree to sell its ownership to the homebuyer for a series of pre-specified monthly payments. The monthly payments include a fair profit for Guidance, but are structured in such a way that they are Shari'ah-permissible "diminishing musharakah " and not impermissible riba (interest). Property taxes and insurance are paid for by the home buyer. If the home buyer wants to sell the property before completing the payments, the home buyer gets to keep all of the capital gain or loss. Guidance only gets its investment back plus a fair rate of return.

For example, suppose that you have decided to purchase a $300,000 house but can only put up $30,000 of your own money. Guidance will invest $270,000 and at first own 90% of the house. However, at the End of each month for the next 360 months you will make a payment of $1,610 to Guidance and gradually purchase the rest of the house from Guidance. At the end of month 360 you will own 100% of the house.

a) What rate of profit is Guidance earing on its investment, expressed as an APR?

b.) What is the present value of the profit payments (10 strip) to Guidance, using the profit rate from part a) as the discount rate?

d) What is the present value of the house purchase (principal) payments (PO strip), using the profit rate from part a) as the discount rate?