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

Theoretical Performance

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: $$ W_n = \frac{ SX((1 + A_F R_F + A_M R_M)^n_-(1+R_I)^n) }{ A_F R_F + A_M R_M - R_I } $$