What is Compound Interest? - Definition, Formula & Examples Video

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  • 0:02 Interest: A Surprise Gift
  • 0:39 Simple Interest
  • 2:54 Compound Interest
  • 4:43 Simple and Compound Interests
  • 5:34 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, find out what compound interest is and what makes it different from simple interest. Then learn the formula for calculating compound interest. Finally, compare both types of interest with a graph that shows the growth in interest.

Interest: A Surprise Gift

I'm giving you a thousand dollars! Well, a thousand dollars of virtual money. But, I'm giving it to you on the condition that you have to keep it in a bank for six months. There are two banks nearby: Simple Savings & Loan and Compound Credit Union. They both have great customer service and similar services. The only difference is that Simple Savings & Loan offers 5% simple interest on its savings account while Compound Credit Union offers 5% compound interest.

What does that mean? Which bank should get your thousand dollars?

Simple Interest

Interest is the money someone is paid at a specified rate for use of cash that has been lent. For example, say a bank advertises a 5% monthly interest rate for its regular savings account. That means that every period, or the amount of time in which the bank pays interest, it will pay that person 5% of the balance just for keeping their money there. Therefore, interest on a savings account increases the amount of money in the account over time. However, interest is also calculated on money that is borrowed. Individuals pay interest to lenders when they borrow money for car, home, and other types of loans.

This example will show money earned through interest by using a savings account. So to calculate the interest at Simple Savings, find 5% of $1,000. To do that, multiply $1,000 * 0.05. 5% of $1000 equals 50. This account will earn $50 every year.

The table below shows the interest calculation for a five-year period. Simple interest would have the money growing fifty dollars per year.

Year Previous Balance Interest New Balance
1 $1,000 $1,000 * 0.05 = $50 $1,050
2 $1,050 $1,000 * 0.05 = $50 $1,100
3 $1,100 $1,000 * 0.05 = $50 $1,150
4 $1,150 $1,000 * 0.05 = $50 $1,200
5 $1,200 $1,000 * 0.05 = $50 $1,250

Just by keeping the money in the bank, the individual earned $250 interest. That's fine. But, wait. When the Simple Savings bank calculates the interest, it keeps using the original value of $1,000. This is called simple interest, a kind of interest in which the bank keeps using the original balance to figure each period's interest.

In fact, the only thing happening is multiplying the original balance by the interest rate and by the number of periods that the money stays in the account. So the formula for calculating simple interest looks like:

I = P * r * t

where P is the principal, or the original balance; R is the interest rate percentage; and T is the number of periods the money stays in the account. So, at Simple Savings:

Interest = $1,000 * .05 * 5

But wouldn't it be nice if the bank used the new, higher balance every year to calculate the interest? That would be the power of compound interest! you not only get interest on the money you deposited but interest on the interest too.

Compound Interest

Say, for example, that in year 2, instead of using the original balance of $1,000, the bank used the new balance of $1,050 to determine the monthly interest. To do this, multiply $1050 * 0.05. This equals $52.50. Even though this new interest is only $2.50 more than the old one, watch what happens.

Year 2's new balance is now $1102.50. So to figure that year's interest, use that new, higher balance instead of the original $1,000 balance. See how this works in favor of the person making the interest? The interest builds up much more quickly because the bank is using a higher balance every year to calculate the new interest. This is called compound interest, a kind of interest in which the bank calculates interest based on the previous balance plus the last period's interest.

Look at the same table but with interest compounded annually instead of simple interest:

Year Previous Balance Interest New Balance
1 $1,000 $1,000 * 0.05 = $50 $1,050
2 $1,050 $1,050 * 0.05 = $52.50 $1,102.50
3 $1,102.50 $1,102.50 * 0.05 = $55.13 $1,157.63
4 $1,157.63 $1,157.63 * 0.05 = $57.88 $1,215.51
5 $1,215.51 $1,215.51 * 0.05 = $60.78 $1,276.29

So instead of $250 from the Simple Savings bank this account earned over $270 at Compound Credit Union. And since the interest snowballs with compound interest, the longer the money is kept in the account, the more quickly the interest grows.

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