# Portifolio Returns

## Assumptions

- $X$ currency/year initial net income
- $R_I$% net income raise every year
- $R_F$% yearly near risk-free real return
- $R_M$% yearly market real return
- Saving $S$% of net income
- $A_F$% of savings invested on risk-free
- $A_M$% of savings invested on market

The total wealth $W$ after $n$ years available at year $n+1$ can be recursively defined by:
$$ W_{n+1} = W_n(1 + A_F R_F + A_M R_M) + SX(1+R_I)^n $$
Solving the recursion using $W_0 = 0$, we get:
$$ W_n = \frac{
SX((1 + A_F R_F + A_M R_M)^n_-(1+R_I)^n)
}{
A_F R_F + A_M R_M - R_I
} $$