Question

What is continuous​ compounding? how does the apy for continuous compounding compare to the apy​ for, say, daily​ compounding? explain the formula for continuous compounding?

Answer 1

Continuous compounding is the mathematical limit that compound interest can reach.

It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.

The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).

Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-

1000 ( 1 + 0.02/365)^365 = $1020.20

with continuous compounding this will be

1000 * e^1 = $2718.28

Explanation:

Answer 2

Continuous compounding is the mathematical limit that compound interest can reach.

It is the limit of the function A(1 + 1/n) ^ n as n approaches infinity. IN theory interest is added to the initial amount A every infinitesimally small instant.
The limit of (1 + 1/n)^n is the number e ( = 2.718281828 to 9 dec places).

Say we invest $1000 at daily compounding at yearly interest of 2 %. After 1 year the $1000 will increase to:-

1000 ( 1 + 0.02/365)^365 = $1020.20

with continuous compounding this will be

1000 * e^1 = $2718.28