7-Investment, salary and Exponential curves
With https://www.desmos.com/calculator , you can plot graphs for the given exponential curves
y=exp (0.0953x)
y=exp(0.1823x)
y=exp(0.2624x)
Observe the differences of heights at x=5,10,15,20 etc on these curves.What do they say about your investments?
These curves are continuous time approximation for compound returns of 10%, 20%,30% respectively.
The exponents are obtained by the force of interest = ln(1+r) formula.
The height difference tell how much one investment is better than the other at each point.
For ex. at 5 years, at 10% , your money would have grown 1.61 times the initial amount,2.48 times if its compounded at 20% annually, 3.71 times if its compounded at 30 percent.
At 20 years, multiples stand at 6.73 times, 38.32times , 190 times initial investment for 10%,20%,30% compounded respectively. Growing investments 30% or even 20% is not easy for 2 decades.
What about the salary? How different is from investment. Unlike investment, you receive salary each year and in normal years, the salary increases at a percentage term based on your current salary.
if you plot the salary it may give you a staircase function. We approximate it using the exponential curves above. The total accumulated salary is the area under the curve. You need to do integrate the curve from 0 to nth year. Roughly, You can think of salary as your current run rate that's plotted in a graph, total salary as total score,which is the area under the run rate graph.
At 20 % compounded one would have obtained e^(20*0.1823)/0.1823 ( integration of e^ax) times initial salary in 20 years period. Its more than 210 times the initial salary. At 10% compounded increment total salary would be around 70 times the initial salary in 20 years.Such kind of exponential growths are not easy to achieve in practise.
Salaries are not smooth over the years.But you can always have some approximations to use mathematical analysis to get a big picture.
We have done analysis so far in nominal terms, without bringing inflation and tax into picture which can dramatically change the story.They could flatten out the curves. Income Tax is applied on nominal amount on interest and salary, not on the real increase. If you have 8 percent interest on FD and is taxed at 30% you effectively get 5.6% . If in FY18 Consumer price inflation is 5% you get 0.6% increase real interest rate. At this rate you can double your purchasing power in 71 years as per 72 rule(72/1.006).
An 8% and 10% increment in nominal terms will turn into a 0.6 percent, 2 percent hike after tax (at slab 30%) and inflation. Stagnant income is a debating point in US as well as economists point out there is no real growth in overall household income for 4 decades. But smart companies do well. All top market cap tech companies are characterised by innovation, scalability ,user friendliness and possessing lot user data. Probably if we focus on some of these aspects we may add value that market finally recognises.
y=exp (0.0953x)
y=exp(0.1823x)
y=exp(0.2624x)
Observe the differences of heights at x=5,10,15,20 etc on these curves.What do they say about your investments?
These curves are continuous time approximation for compound returns of 10%, 20%,30% respectively.
The exponents are obtained by the force of interest = ln(1+r) formula.
The height difference tell how much one investment is better than the other at each point.
For ex. at 5 years, at 10% , your money would have grown 1.61 times the initial amount,2.48 times if its compounded at 20% annually, 3.71 times if its compounded at 30 percent.
At 20 years, multiples stand at 6.73 times, 38.32times , 190 times initial investment for 10%,20%,30% compounded respectively. Growing investments 30% or even 20% is not easy for 2 decades.
What about the salary? How different is from investment. Unlike investment, you receive salary each year and in normal years, the salary increases at a percentage term based on your current salary.
if you plot the salary it may give you a staircase function. We approximate it using the exponential curves above. The total accumulated salary is the area under the curve. You need to do integrate the curve from 0 to nth year. Roughly, You can think of salary as your current run rate that's plotted in a graph, total salary as total score,which is the area under the run rate graph.
At 20 % compounded one would have obtained e^(20*0.1823)/0.1823 ( integration of e^ax) times initial salary in 20 years period. Its more than 210 times the initial salary. At 10% compounded increment total salary would be around 70 times the initial salary in 20 years.Such kind of exponential growths are not easy to achieve in practise.
Salaries are not smooth over the years.But you can always have some approximations to use mathematical analysis to get a big picture.
We have done analysis so far in nominal terms, without bringing inflation and tax into picture which can dramatically change the story.They could flatten out the curves. Income Tax is applied on nominal amount on interest and salary, not on the real increase. If you have 8 percent interest on FD and is taxed at 30% you effectively get 5.6% . If in FY18 Consumer price inflation is 5% you get 0.6% increase real interest rate. At this rate you can double your purchasing power in 71 years as per 72 rule(72/1.006).
An 8% and 10% increment in nominal terms will turn into a 0.6 percent, 2 percent hike after tax (at slab 30%) and inflation. Stagnant income is a debating point in US as well as economists point out there is no real growth in overall household income for 4 decades. But smart companies do well. All top market cap tech companies are characterised by innovation, scalability ,user friendliness and possessing lot user data. Probably if we focus on some of these aspects we may add value that market finally recognises.
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