Continuous Compound Interest Formula

Definition

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
 

 

Example Problem

An amount of $2,340.00 is deposited in a bank paying an annual interest rate of 3.1%, compounded continuously. Find the balance after 3 years.

Solution

Use the continuous compound interest formula, A = Pe rt, with P = 2340, r = 3.1/100 = 0.031, t = 3. Recall that e stands for the Napier's number (base of the natural logarithm) which is approximately 2.7183. However, one does not have to plug this value in the formula, as the calculator has a built-in key for e. Therefore,

Example Solution

So, the balance after 3 years is approximately $2,568.06.

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