When X→∞ (approaching infinity), (1+I/x) x = E I (this is the definition equation of e), the final formula can be obtained by substitution.
Extended data
Continuous compound interest: In extreme cases, the principal C0 will bear interest according to compound interest in an infinitely short time.
Assuming that the current interest rate is δ and e is a natural constant, the final investment value Fv = c0×E(δt) after t years of investment.
Continuous compound interest. The relationship between annualized percentage return and effective annual interest rate;
The actual annual interest rate of EAR,
R annualized percentage interest rate.
The relationship between real interest rate, nominal interest rate and inflation rate;
Real interest rate r
Nominal interest rate r
Inflation rate I
Under other circumstances?
This is only an approximation.
But it is an identity under continuous compound interest:
Baidu Encyclopedia-Continuous Compound Interest