## Compound Interest Calculator

## Simple Compound Interest Calculator Online

## Compound Interest Calculator

**Compound Interest Calculator: Understanding the Power of Compound Interest**

**What is compound interest?**

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. In simple terms, it’s interest on interest, and it allows your investments to grow exponentially over time. Unlike simple interest, which only calculates interest on the principal amount, compound interest takes into account the interest earned over previous periods as well.

**Example:** Let’s say you invest $1000 in a savings account with an annual interest rate of 5%. After one year, you’ll earn $50 in interest. In the second year, you’ll earn interest not only on the initial $1000 but also on the $50 interest earned in the first year. This compounding effect continues to grow your investment over time.

**Different compounding frequencies:**

Compounding frequency refers to how often the interest is added to the principal amount. Here are some common compounding frequencies:

**Annually (APY)**: Interest is compounded once per year.**Semiannually**: Interest is compounded twice per year.**Quarterly**: Interest is compounded four times per year.**Monthly (APR)**: Interest is compounded twelve times per year.**Semimonthly**: Interest is compounded twenty-four times per year.**Biweekly**: Interest is compounded twenty-six times per year.**Weekly**: Interest is compounded fifty-two times per year.**Continuously**: Interest is compounded infinitely, meaning it’s calculated and added continuously.

**Compound interest formulas:**

The compound interest formula is given by:

*A*=*P*(1+*r/*n)^{nt}

Where:

*A*= the future value of the investment/loan, including interest*P*= the principal investment amount (the initial deposit or loan amount)*r*= the annual interest rate (in decimal)*n*= the number of times that interest is compounded per year*t*= the number of years the money is invested/borrowed for

**Basic compound interest:**

Basic compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods. It is also called “interest on interest” because it makes the principal amount grow faster than simple interest, which is calculated only on the initial principal. The formula for basic compound interest is:

CI = P (1+r/n)^{nt} – P

Where:

- CIis the compound interest
- Pis the initial principal
- r is the annual interest rate
- n is the number of times interest is compounded per year
- t is the time in years

For example, if you invest $1000 at 10% interest compounded annually for 5 years, the compound interest will be:

So, you will earn $610.51 in compound interest and your total amount will be $1610.51 after 5 years.

You can learn more about compound interest from these sources:

**Continuous compound interest:**

Continuous compound interest is the interest calculated on the initial principal and the accumulated interest from previous periods, but with an infinite number of compounding periods. It is the limit of compound interest as the frequency of compounding approaches infinity. The formula for continuous compound interest is:

A = Pe^{{rt}}

Where:

- A is the final amount
- P is the initial principal
- e is the mathematical constant approximately equal to 2.7183
- r is the annual interest rate
- t is the time in years

**Rule of 72**

The Rule of 72 is a quick way to estimate how long it will take for an investment to double at a fixed annual rate of interest. It’s calculated as:

Years to double=72/Annual interest rate

**History of Compound Interest:**

Compound interest has been used for centuries, dating back to ancient civilizations like Babylon and Egypt. It’s a fundamental concept in finance and has played a significant role in the growth of economies and the accumulation of wealth over time.

In conclusion, compound interest is a powerful tool that allows your investments to grow exponentially over time. By understanding the different compounding frequencies, formulas, and the Rule of 72, you can make informed decisions about your investments and financial planning.