Infinite money hack: Euler’s number and compound interest
Compound interest is a powerful concept that allows individuals to grow their wealth over time. It's based on the idea that the interest earned on an investment can be reinvested to generate even more interest, creating a "snowball" effect that can lead to significant growth.
Subscribe: https://bit.ly/polymathematic | Enable ALL push notifications 🔔
Euler's constant, denoted by the symbol "e," is a mathematical constant that represents the base of the natural logarithm. It's a fundamental concept in mathematics, and it appears in many different contexts, including in the formula for compound interest.
In this video, I take a look at a thought experiment that reveals the connection between continuously compounding interest and Euler's number.
One of the key things to understand about compound interest is that it's calculated on the principal amount of an investment, as well as on any interest that has already been earned. This means that the more time that passes, the more interest is earned on the initial investment, which in turn leads to even more interest being generated.
To calculate compound interest, we use the following formula: A = P (1 + r/n) ^ nt
In this formula, "A" represents the total amount of money that will be earned over time, "P" is the initial principal amount, "r" is the interest rate, "n" is the number of times that the interest is compounded per year, and "t" is the number of years that the investment will be held.
If you let the number of times the interest is compounded per year grow toward infinity, this formula changes into A = Pe^ rt. Euler's constant, "e," appears in this formula as the base of the exponent. This constant is approximately equal to 2.71828, and it's an important concept in mathematics that arises in many different contexts.
This may seem counterintuitive, but it's a direct consequence of the properties of Euler's constant and the way that compound interest is calculated. Essentially, Euler's constant represents the maximum rate at which money can grow over time when compounded continuously, which means that it's a powerful tool for understanding the potential growth of an investment.
#compoundinterest #eulersconstant #calculus
Follow Tim Ricchuiti:
TikTok: / polymathematic
Twitter: / poly_mathematic
Instagram: / polymathematicnet
Reddit: / polymath-matic
Facebook: / polymathematic
Watch more Math Videos:
Math Minis: • Math Mini
Math Minutes: • Math Minutes
Number Sense: • Number Sense (UIL / PSIA)
MATHCOUNTS: • MATHCOUNTS