I just read that increase in aggregate demand increases investment for a given interest rate. How is it possible because when aggregate demand increases, this shifts the demand for money to the right leading to higher interest rates. Higher interest rates should reduce investment. Am I correct in with my argument? And help will be appreciated.
Once again, the fixed thing is interest rates. There are numerous ways in which a government can control an interest rates: one of which is to control the money supply. I feel that in your case, you are assuming that the amount of money in the economy and the speed of money flow is fixed. However, we can control the interest rates by controlling the money supply. When we want to make an interest rates at a fixed term, we want to pump more money into the economy and thus increasing the supply of money and keeping the interest rates as low as it used to be. Thus it is possible for that to happen. Please note that I have also assume that the interest rates dixed and the economy is not running at the intermediate or full capacity
An investment project has expected returns $R$ and expected costs $C$. Investments will happen as long as $R > C$.
An increase demand will increase the potential return from projects, $R$. An increase in interest rates will increase the costs $C$.
Now all that matters is whether the change in $R$ through increased in demand is larger than the increase in $C$ through the interest rates. I would argue that the demand for money argument that you are bringing has rather second order effects.
To conclude, while your channel certainly exists, it's not strong enough to overcome the positive investment effects of increased aggregate demand.