How much do you need to invest on a monthly basis into a $401$K$,$ no match, if you started when you're $30$ years old and desire to have a $$500,000$ balance in the year you turn $67.$ Then calculate it if you started at $40$ and then $50$ years old. As an example, here is the calculation for a $30$ year old.

$1)67-30=37$ years

$2)$ Assume investment return of $8\%$

$3$ Future value $+$ $$500,000$

The amount needed to save on a monthly basis $=$ $$205\mathrm{.}18$ monthly or $$2,462\mathrm{.}16$ annually.

Note: I kept both the period and interest rate at a full year. Then, I divide the annual result by twelve.

What if I started at $40$ years old? What if I started at $50$ years old? What critical lesson can you learn from this exercise?