Rohit – You know what, I don’t think I can retire early. I think only people who earn more than Rs. 1 crore can retire early. This is not just the story of Rohit but of countless people I have spoken with. What people fail to understand is that income is the least important thing for financial independence, it is your expense that determine everything. Reasons being : a) Lower expense mean a higher savings rate and b) Lower expense mean that you need a much smaller retirement portfolio (since you can live by spending less). I have talked about it more in my post here. If your income is above a minimum amount then income doesn’t matter for financial independence.

But today let us use mathematics to prove that expense is more important than income for financial independence.

**Using mathematics to prove why income doesn’t matter**

You might have heard about the 4% safe withdrawal rule, if not read about it in my post here. Idea is that to be financially independent 4% (or whatever it is for you) of investment/retirement portfolio ** (P)** must be enough to cover expenses

**.**

*(E)*Hence, 4% x **P **=** E** or 0.04 x **P **=** E**

Suppose income is represented as ** I** and savings rate (i.e. savings/income * 100) as

**, then:**

*S***E**=

**I**x (1-

**S**).

But we already know that **E **= 0.04 x **P**.

**Hence, 0.04 x P = I x (1-S)**

Now, we know that **P** or total retirement portfolio is nothing but total money saved + interest amount. Hence, **P **= Income (**I**) x Savings rate (**S**) x [((1+**R**)^N – 1)/**R**], where **R **is the returns and N is the number of years.

What we have then is : 0.04 x **I **x **S** x [((1+**R**)^**N** – 1)/**R**] = **I** x (1-**S**)

If you look at the equation carefully, you can see that **I **(income) on both left and right hand side cancel each other. Hence, we are left with the following:

**0.04 x S x [((1+R)^N** **– 1)/R] = (1 – S)**

### Hence proved

Above equation proves that income on it own doesn’t matter. The saving rate is dependent more on how much you spend, rather than how much you earn. Reason being, that most of us don’t see a sharp increase in income (very rarely people who were earning Rs. 6 lakhs an year ago start earning Rs 1 cr). What happens in most of the cases is that our income increases gradually (10-20% per year) and more often than not our expenses increase in line (10-20%). This means that most of us are never increasing our savings rate even though income is increasing. Why, you ask. That is because we don’t follow the philosophy of buy what you need, not what you want.

To summarize, below is how savings rate (which essentially depends on your expense) affects your years to financial independence.

But with even basic expenditure like rent, food (we eat at home), transport and school fee for kids, my saving rate cannot be more than 25-30%. So income does play a part.

Hi Abhineet,

Thank you for the response. I agree that income does play a role (for example if my monthly income is Rs. 25000 in a city like Delhi, then it is unlikely that my saving rate can be more than 10-20%), however, the point I am trying to make is that as the income rises people tend to increase their expenditure rather than increasing the savings rate. This leads to a two-fold problem a) One saves less and hence takes a longer time to reach the target goal b) if expenses increase more than assumed inflation then the target goal also increases, thus taking even more time to reach it. The reason target goal increases is because if one is consistently spending a certain amount then it is unlikely that immediately post retirement one would be able to substantially cut-down on that amount, as the life-style gets adjusted to spending that much amount. Hope this helps.

-Mr.FIREForty