Blog (mostly math)

Investments

Ref: “The simple path to wealth” by Collins.

Link to a talk: Link.

Link to blog post: Link.

ROUGH NOTES (!)
Updated: 20/11/25

Money is valuable.

Money brings you freedom. Note that work can be enjoyable when you aren’t effectively a slave to it.

Avoid debt.

Spend less than you earn - invest the surplus - avoid debt.

A mutual fund is a collection of investors’ money that fund managers use to invest in stocks, bonds, and other securities.

An index fund is a type of investment that tracks the performance of a specific benchmark like the S&P 500. Instead of picking individual stocks, an index fund tracks the performance of a specific market benchmark—or “index”, like the popular S&P 500 Index—as closely as possible.

Eg: The author considers the following scenario.

P earns ${ $ 25,000 }$ every year.

P organised his life such that he can live on ${ $ 12, 500 }$ anually.

Consider P to be financially independent when P can live on ${ 4 \% }$ of his net worth each year.

Note that P needs a net worth such that ${ \frac{4}{100} \times (\text{Net worth}) = $12, 500 }$ to be financially independent.

Note that P needs a net worth of ${ $ 312, 500 }$ to be financially independent.

It turns out in ${ 1975 - 2015, }$ VTSAX (Vanguard Total Stock Market Index Fund) had an average annual return of ${ 11.9 \% . }$

Link to VTSAX page: Link.

P invests ${ $12,500 }$ each year. Assuming ${ 11.9 \% }$ annual return, P will be financially independent (${ $ 317,175 }$) in around ${ 11.5 }$ years.

Link to investment calculator: Link.

After ${ 11.5 }$ years, P starts to spend his full earning ${ $ 25,000 }$ every year, and leave the ${ $ 312, 500 }$ alone.

In ${ 10 }$ more years, the amount will have grown to ${ $ 961, 946 . }$

Link to investment calculator: Link.

That amount yields ${ $ 38, 478 }$ a year at ${ 4 \% }$ withdrawal rate.

P can not only quit working, but give himself a substantial raise.

Note that many simplifying asssumptions were made. Ignored taxes, ignored increase in income, etc.

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