Continuously Compounded Interest Equation Math

A woman deposits 5 000 into a savings account with continuously compounded interest at an annual rate of 4 5.

Continuously compounded interest equation math. The continuous compounding formula is used to determine the interest earned on an account that is constantly compounded essentially leading to an infinite amount of compounding periods. P principal dollars invested. Fv 1 000 e 0 08 1 000 1 08328 1 083 29. Like it just suddenly clicked.

T term of investment in years example. N the compound interest equation takes the form. The general compounding formula is a p left 1 frac r n right nt. P c e rt.

As can be observed from the above example the interest earned from continuous compounding is 83 28 which is only 0 28 more than monthly compounding. In my second equation you can see how the thing inside the large parens is of this form and therefore we can use the authors statement to jump right to the limit. To calculate continuously compounded interest use the formula below. Begingroup i did that so that i d get a limit that looked like the one that the authors had given 1 frac 1 n n.

Another example can say a savings account pays 6 annual interest compounded continuously. A p e rt continuous compound interest formula where p principal amount initial investment r annual interest rate as a decimal t number of years a amount after time t the above is specific to continuous compounding. In the formula a represents the final amount in the account that starts with an initial principal p using interest rate r for t years. Formula for compounded interest.

The effect of compounding is earning interest on an investment or at times paying interest on a debt that is reinvested to earn additional monies that would not have been gained based on the principal. S final dollar value. General compound interest takes into account interest earned over some previous interval of time. The importance of this article is to get you excited about compound interest and to teach you the ability to understand the continuous compound interest formula.

General compound interest principal 1 annual interest rate n n time. R annual interest rate. N is the number of times interest is compounded in a year. The formula truly is fairly simple to understand and in my case once i got it i got it.

Continuous compound interest when interest is compounded continually i e. Following is the formula to calculate continuous compounding.