Temporal Growth Curve
Wealth Evolution by Period
| Period (Year) | Invested Capital | Simple Interest Balance | Compound Interest Balance | Actual Difference (Gain) |
|---|
Visualize the power of interest on interest in your wealth. Compare the differences in return rates between the simple interest regime (constant linear growth) and the compound interest regime (accelerated exponential growth) with monthly contributions.
| Period (Year) | Invested Capital | Simple Interest Balance | Compound Interest Balance | Actual Difference (Gain) |
|---|
Financial mathematics divides capital growth into two basic regimes of financial capitalization:
In Simple Interest, the yield is calculated always on the initial capital. The amount received as interest in each period is fixed and linear. If you have $1,000.00 earning 10% per annum under simple interest, you will earn exactly $100.00 every year. Past profits do not generate new profits; it is a growth in a straight line.
In Compound Interest, the interest from each period is incorporated into the total capital to calculate the yield for the next period (the famous "interest on interest"). If you have $1,000.00 at 10% per annum under compound interest:
Almost the entire financial market and investments operate under the Compound Interest regime (CDBs, savings, Treasury Direct, investment funds, and stocks). Simple interest is more common in very specific commercial transactions, fixed coupons, and short-term installments.
Time is the most important factor in the formula. Since the growth is exponential, the greatest gains occur in the final stages of the investment. Doubling the investment term usually generates much more than double the final wealth, due to the extreme accumulation of interest on interest at the end of the curve.
Inflation acts in the opposite way to compound interest, eroding the purchasing power of your money exponentially. Therefore, when planning long-term investments, it is essential to discount the estimated inflation (work with the real rate) to know the actual purchasing power you will have in the future.