The author has a feew things wrong. First of all, growth due to compounding is geometric, not exponential. He has the two used interchangeably when they are vastly different over any reasonable timeframe.
Second, compounding isn't magic. Invest $1,000 at 5% annual ror over 25 years, and your final amount is -$3400. To actually grow exponentially as the author wants, an investor has to contribute additional principal on a periodic basis. Now, when you combine those two ideas, the question becomes: With my extra $200, should I buy more of the same stock or some of new stock? That's where diversification fits into an investor's strategy, and as copious amounts of data show, increased diversification has a higher annual ror compared to fixed asset investing. In fact, the ultimate diversification strategy is to buy a small piece of the total market aka index funds, and the historic annualized ror shows how effective this strategy is.
If I invest $1,000 at 5% annual return, I expect to have 1000 * (1.05)^n after n years. That fits my definition of exponential - time is an exponent in the formula.
My quibble was about geometrics vs exponential, but beyond the mathematical distinction of discreteness, they are equivalent, so I stand corrected on that front.
Second, compounding isn't magic. Invest $1,000 at 5% annual ror over 25 years, and your final amount is -$3400. To actually grow exponentially as the author wants, an investor has to contribute additional principal on a periodic basis. Now, when you combine those two ideas, the question becomes: With my extra $200, should I buy more of the same stock or some of new stock? That's where diversification fits into an investor's strategy, and as copious amounts of data show, increased diversification has a higher annual ror compared to fixed asset investing. In fact, the ultimate diversification strategy is to buy a small piece of the total market aka index funds, and the historic annualized ror shows how effective this strategy is.