I have this equation $$X(1+0.2)^Y$$ Which is simply adding 20% every $Y$ month for the $X$. For example $$100(1+0.2)^1 = 120$$ $$100(1+0.2)^2 = 144 $$ What I want to do is cutting or rebating 10 every month so it becomes the first month $110$ instead of $120$ and the second one the equation goes like this $110(1+0.2)^2 = 132$ instead of $144$
I tried to do this $$100(1+0.2)^1-10 $$ But it's just cutting $10$ from the total, Which is not exactly what I want it to do.
Please help me to make the correct equation.
The question is unclear, but if I understood correctly, you want to grow 20% and then cut 10 each month, so that if $A_t$ is amount at the end of month $t\geq 1$, we have
$$A_t=RA_{t-1}-r,$$
your problem being the case where $$A_0=100\\ R=1.2\\ r=10.$$
Induction shows the general solution to this recurrence relation is $$A_t =A_0 R^t-r\frac{R^t-1}{R-1},R\neq 1\\ A_t =A_0-rt,R= 1.$$
UPDATE: As requested in the comments, if the problem is to grow 20% each month and then also cut 10 percent each month, the problem is simpler. The amount at the end of month $t\geq 1$ is then given by exactly the same formulas as above, except where
$$A_0=100,R=(1+0.2)(1-0.1)=1.08,r=0.$$