E and compounding

e≈2.718

Calculate a compound interest example, set the principal p, the annual interest rate is r, the monthly interest is calculated, the monthly interest is R/12, then the principal and interests of one year are altogether:

P (1+R/12) 12=PQ

When the time interval for the calculation of compounding is getting smaller, according to the above limit formula, the multiplication of the principal is Q=er,

In the case of continuous compounding continuous compounding, the principal and interest of one year is per, and the principal and the post of T years is pert

In fact, there are very few extreme interest rates that use continuous compounding, the advantage of a continuous framework is that its models are easily analyzed with mathematical tools.

E and compounding