Hi guys, I’ve been practicing tests online and sometimes I can’t find the right answer to a question or don’t know how they got to the conclusion or basically need a shortcut. I was thinking if there were more ppl like me and need help explaining then we could help each other out
There’s this one that I managed to solve but my method was quite lengthy  is there a faster way to solve this or am I doomed each time I get this in a test?
This one is from SHL
XYZ Company purchased a new machine in March at $50K and is using the profits to pay it off. Profits in March were $7876. If the profits increase 2% from the previous month, in what month will the machine be completely paid off?
A: June
B: July
C: August
D: September
E: October
So here are my 2 methods:

short but relies on estimation therefore not entirely reliable. $50K / $7876 = 6.34. Without increase they’ll have collected $47,256 in August, missing $2,744 to hit the $50K. 2% increase each month is appx. $157 each month which isn’t high enough to make the target therefore they need another month > answer is September.

Basically hit 7876 + (7876 x 1.02) + (7876 x 1.02^2) …etc. till I hit $50K
There must be a faster & more reliable method than this surely???
Appreciate any help!