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?

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