How to calculate the spending multiplier from a given set of equations?
Your friend is right. If you look at the initial investment equation, and comparing it to your definition, you have:
$$I=900+(0)Y-50i$$
So $d_{1}=0$ and $c_{1}=0.8(0.75)$ and thats why you get the spending multiplier as $\frac{1}{0.4}$