Another way of thinking of the formula is taking it as a geometric progression as in maths: remember Multiplier (k) = 1/MPS = 1/1-MPC = 1/1-r
Where a = amount of government spending and r = MPC
So assume MPC, the marginal propensity to consume is 0.8, i.e, 80% of extra/additional income earnt will be consumed by the consumers.
So if the government spends $10,000 and MPC in a city is 0.8.
Then the first round of spending will be $10,000 on familes (e.g.)
The families will go and spend (0.8 x 10,000) $8000 out of their $10,000 on clothes
Clothes shop owners who receive the $8000 will spend (0.8 x 8000) $6400 on cotton to make their clothes
etc. etc.
So the effective total amount will be: $10000 + $8000 + $6400 + .... = k (multiplier) x $10000
But the multiplier k = 1/1-MPC = 1/1-0.8 = 5
So the total amount = 5 x $10,000 = $50,000
Ok, hope you get all of that - this is one of the most interesting parts in the eco syllabus so have fun with it