What is the relationship between the demand for loanable funds and investment? If the demand for loanable funds decreases, investment increases because the real interest rate decreases. Isn't that a contradiction, because loanable funds are used for investment, and a decrease in demand for loanable funds must come from a decrease in investment?
Assuming loanable funds are all used for investment, loanable funds = investment.

The interest rate can be though of as the price for loanable funds. Take a look at the following graph.



You can think of the change from point A to C in two steps, with B as the intermediary, even though in reality both steps probably happen simultaneously.

First the shift in demand from D to D2 (decrease in demand for loanable funds) is reflected by the move from A to B. Price has not yet changed at this point.

Then, a new equilibrium is reached with quantity demanded moving down the new demand curve (as price decreases) to point C. In this step price decreases so the quantity demanded actually increases. But it does not reach the quantity demanded at the original point A. 

So as the demand curve shifts to the left both price and quantity demanded decrease.