80% of the $800,000 purchase price=$640,000.
The down payment is 20% of the purchase price=$160,000.
Add to this expenses of $40,000=$200,000.
This would need to be the return on the investment between 1 Jan 2013 and 1 Jan 2015 (24 months).
The annual investment rate is 6%, so the monthly rate is 6/12=½% or 0.005.
The first payment accumulates 24 months' interest compounded monthly=1.00524m, the second payment accumulates 23 months' interest, the third payment 22 months' interest and so on. The last payment on 1 Dec 2014 grows to 1.005m by 1 Jan 2015.
When we add all these together we get:
m(1.00524+1.00523+1.00522+...+1.005)=1.005m(1.00524-1)/0.005=200000 (sum of geometric series),
m=1000/(1.005(1.00524-1))=$7,825, the monthly payment.