Could you explain how compound interest works and its implications for long-term investments? For example, if I were to invest $10,000 now with a 7% annual return rate, how much would it grow over 20, 30, and 40 years? Can you also explain how reinvesting dividends impacts the overall growth in such scenarios?
Sure, compound interest is when the interest you earn on an investment begins to earn interest itself. It’s one of the most powerful concepts in finance. It has the ability to multiply money over time and consists of reinvesting earned interest back into the original investment.

Let’s take your example of $10,000 invested at a 7% annual return rate.

After 1 year, you’d earn $700 interest ($10,000 * 7%), giving you a total of $10,700.

In the 2nd year, you would earn interest not just the initial $10,000 (the principal), but also on the $700 interest you earned in year 1. So, the interest for year-2 would be $749 ($10,700 * 7%).

This effect would compound over time, so here’s how it would look like for the durations you asked for:

- After 20 years, your investment would grow to about $38,696.
- After 30 years, it increase to around $76,123.
- After 40 years, it would become approximately $149,745.

So, the longer you leave your money and let the interest compound, the more money you'll have in the end.

Now, as for reinvesting dividends - it increases the overall growth of investment as the reinvested dividends start to earn their own returns. If you chose to receive the dividends as cash instead, only your initial investment would earn returns, which would result in less total return over the long run. It's kind of 'supercharging' your compound interest.