Understanding Compound Interest | Calculation and Examples with Continuous Compounding

compound (continuous) interest

Compound interest is a concept in mathematics and finance that refers to the interest generated on an initial amount of money, called the principal, which is reinvested to earn additional interest

Compound interest is a concept in mathematics and finance that refers to the interest generated on an initial amount of money, called the principal, which is reinvested to earn additional interest. Essentially, compound interest allows the interest earned to be added to the principal, creating a new, larger amount from which interest is calculated.

In the case of compound interest, the interest is calculated and added to the principal at regularly scheduled intervals, such as annually, semi-annually, quarterly, monthly, or even continuously. The interest is then recalculated based on the increased principal amount.

Continuous compounding is a special case of compound interest, where the interest is continuously compounded over time. This means that the interest is added to the principal infinitely many times throughout the given time period, resulting in the highest possible amount of interest earned.

The formula to calculate the final amount with continuous compound interest is given by:

A = P * e^(rt)

Where:
A is the final amount after time t,
P is the principal amount,
e is a mathematical constant approximately equal to 2.71828,
r is the interest rate as a decimal.

For example, let’s say you invest $1,000 at an annual interest rate of 5% with continuous compounding for 5 years. By applying the formula, we have:

A = $1,000 * e^(0.05 * 5)
A = $1,000 * e^(0.25)
A ≈ $1,000 * 1.284
A ≈ $1,284.03

Therefore, at the end of 5 years, your investment would grow to approximately $1,284.03 with continuous compound interest.

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