Hi Andre!
Shinjiru(信じる) rather means "I am going to believe/trust" in Japanese.
Here is a funny example:
"Honestly, I didn't cheat on you!"
"...Ok... Shinjiru yo"
Shinjiru implies that you haven't believed at first or before but you are going to.
On the other hand, Shinjite iru(信じている) means you are "believeing" and you won't change your mind.
"Watashi wa nihon ga jishin kara tachinaoru to shinjite iru"
I believe Japan will recover from the earthquake
This implies that you haven't doubted that Japan won't recover from the earthquake. You are believing Japan will recover.
Hope this helps :)