5 ms·

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 vas

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.

AnimalMuppet 2y ago
What's your definition of exponential? 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.
- mystified5016 2y ago
  It's really not a matter of interpretation. Geometric and exponential growth are well defined mathematical concepts. Geometric functions can have exponents. This does not imply the function is exponential. These are very different things. https://en.m.wikipedia.org/wiki/Exponential_growth https://en.m.wikipedia.org/wiki/Exponential_growth
  - AnimalMuppet 2y ago
    The page you cite gives the formula for exponential growth as: {\displaystyle x_{t}=x_{0}(1+r)^{t}} Um, right, let me translate that into something that can display here: x(t) = x(0) * (1+r)^t Well, if you look at the formula I gave for compound interest: x(t) is the value at time t, x(0) is the value at time 0, namely $1000, (1+r) is 1.05, and t = n, the number of years. So, from your own cited article, how is that not exponential? Or were you agreeing with me, and disagreeing with glitchc?
    - glitchc 2y ago
      My quibble was about geometrics vs exponential, but beyond the mathematical distinction of discreteness, they are equivalent, so I stand corrected on that front.

AnimalMuppet 2y ago

What's your definition of exponential? 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.

mystified5016 2y ago
It's really not a matter of interpretation. Geometric and exponential growth are well defined mathematical concepts. Geometric functions can have exponents. This does not imply the function is exponential. These are very different things. https://en.m.wikipedia.org/wiki/Exponential_growth https://en.m.wikipedia.org/wiki/Exponential_growth
- AnimalMuppet 2y ago
  The page you cite gives the formula for exponential growth as: {\displaystyle x_{t}=x_{0}(1+r)^{t}} Um, right, let me translate that into something that can display here: x(t) = x(0) * (1+r)^t Well, if you look at the formula I gave for compound interest: x(t) is the value at time t, x(0) is the value at time 0, namely $1000, (1+r) is 1.05, and t = n, the number of years. So, from your own cited article, how is that not exponential? Or were you agreeing with me, and disagreeing with glitchc?
  - glitchc 2y ago
    My quibble was about geometrics vs exponential, but beyond the mathematical distinction of discreteness, they are equivalent, so I stand corrected on that front.