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vfiekz [6]
3 years ago
7

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

xplain the formula for continuous compounding?
Mathematics
2 answers:
mart [117]3 years ago
7 0

Answer:

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  

Step-by-step explanation:

aliya0001 [1]3 years ago
4 0
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  
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