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**On This Page:**

- what is compound interest
- compound interest formula
- compound interest examples
- compound interest vs simple interest
- how to estimate compound interest
- compound interest definition

## What Is Compound Interest

Compound interest is Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest is typically thought of as “interest on interest”. Compounding interest will make your investments grow much faster than simple interest, and it grows exponentially over time.

## Compound Interest Formula

A basic compound interest formula would look like the following:

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

Where…

P = principal amount (the initial amount you borrow or deposit)

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n = number of times the interest is compounded per year

## Compound Interest Examples

Let’s take a look at a very basic compound interest example in which an amount of$2000 is deposited in an account that is earning an annual interest rate of 5% compounded quarterly and we want to know what the balance will be after the interest has been compounded for 5 years:

Using the compound interest formula, we have that

P = 2000, r = 5/100 = 0.05, n = 4, t = 5.

Thus, the formula would look like:

**A = 2000 * ( 1 + .05/4)(4*5)**

So the value after 5 years would be: ~$2,564

## Compound Interest vs Simple Interest

Compound interest is “interest on interest”. This means that if you have $1000 in your account earning 10% interest compounded annually, at the end of the first year your account will be worth $1100. The second year you will earn 10% of the total account value – meaning you earn interest on your initial principal plus the interest you have earned.

Simple interest, however only pays you interest on the initial principal. So in the example above, each year you would earn $100 in interest because the amount of interest you are paid always is calculated off of the amount you originally deposited and NOT the total value of your account.

## Compound interest is the eighth wonder of the world

According to Albert Einstein, coupound interest int he eighth wonder of the world. He who understands it gets it, he who does not, pays it.

## What Types Of Savings Accounts Offer Compound Interest?

Most of your regular savings vehicles offer interest that is compounded. Most CDs and money market accounts will calculate compounded interest on your balances.

## How To Estimate Compound Interest

One easy method you can use to calculate compound interest is the rule of 72. This simple equation will let you know how long it will take your money to double in value based on the interest rate.

So, let’s say you have an account earning 10% interest compounded annually. Using the rule of 72, we can estimate that your account value will double in 7.2 years.

## The Power Of Compound Interest

We all remember the story or have been offered as a child the option to work for a penny a day and have it doubled every day. Most of us scoffed at the idea not realizing that in a few short days we’d be raking in the cash. Sure it starts out really small and who wants to work for a measly $.32/day. However, when we realize that the offer is a 100% interest rate compounded daily we realize we have made a grave error.

Sure this example of compound interest is extreme, but it should not be discounted. When we’re talking compounded interest, every percentage point counts as over the course of 40 or 60 years, one to two percent can result in millions of dollars lost.

## How To Use the Concept of Compound Interest When Investing in Stocks (DRIP)

The stock market does not really lend itself to compounding interest principles, however one method of obtaining these kinds of results is through DRIPs or Divident Re-Investment Plans. If you have a good growth stock (a company growing at 8%/year) and that pays a 3-5% yield, you could set yourself up for some nice gains and mimic a compound interest account.

Let’s say you purchase $5000 worth of stock of a company that is growing at a steady 8%/year and pays a 4% dividend quarterly. This means you would receive roughly $50/quarter in dividends. If you purchased more stock in the same company with your dividends you would not only get the benefit of a 4% compounded interest rate, you’d also get any gains due to the increase in stock price.

Dividend Reinvestment Plans (DRIPs), are currently offered by about 1000 companies and various mutual funds. DRIPs are programs which allow current shareholders to purchase stock directly from the company. Investors purchase shares with dividends that the company reinvests for them in additional shares.

## Compound Interest Definition

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on. This addition of interest to the principal is called compounding.