Why Your 401k match isn't what you think *math inside*
Why Your 401k Match Is Not What You Think
I am going to do a mathematical example to show you the real return of your 401k contribution.
Let's assume I make $60,000 per year (a modest starting salary for my major). My company matches dollar for dollar my 401k contributions up to 4% of my salary.
4% of 60,000 is 2,400
So if I contribute 2,400 my company adds in another 2,400 to put me at 4,800.
When I graduate from college and get this job, I will be approximately 22.5 years old. If I withdraw this investment when I am 59.5 years old, I will have waited 37 years.
Fv = Pv * (1 + R)^n
Fv = 4800 * (1 + 0.05)^37 (assuming you can make 5% return through stocks/mutual funds)
Fv = 29,190.75
This is the total value of your contribution after 37 years.
We are going to use this value to find the value of each individual dollar after 37 years and call this value “A”.
A = Fv / C
“C” is your after tax dollars. Since most people will want to compare pre tax 401k returns to after tax real estate returns, it make since to find the equivalent after tax value.
According to https://smartasset.com/taxes/income-taxes#xar90xIn5V my total effective income tax is 26.3%. (Make sure you understand the difference between marginal and effective income tax.)
So, $2,400 in 401k would be equal to $1,768.8 in after tax dollars which could be invested in real estate.
C = 2400 - 2400*0.263
C = 1,768.80
Now:
A = 29,190.75 / 1,768.80
A = 16.50
This means that every dollar invested is worth 16.50 dollars after 37 years.
To find the average compounded interest rate (y) for the 37 years we use:
(1 + y)^n = A
Solve for y:
y = A^(1/n) - 1
y = .0787 or 7.87%
This means that from your initial contribution of $2,400 you made a 7.87% return per year for 37 years. Remember, we assumed that you could make 5% return through stocks/mutual funds, so the 401k increased your yearly return by 2.87%.
Or you could view this as the 2,400 contribution provides the exact same return as a 1,768.80 after tax real estate investment that had a 7.87% Internal Rate of Return.
The condensed formula is:
y = ((((Pv*(1 + R)^n) / C)^(1 / n)) - 1) *100
Here's what happens when you plug this function into a graphing calculator with the variables we used.
The Y-axis is the yearly return and the X-axis is the number of years. Notice that the longer you have to wait to withdraw your 401k, the lower your yearly return is. Try it with your own personal variables and sorry this was so long. Also, your yearly return will be less if your company only matches 50 cents on every dollar of yours.