# Compound Interest Basics

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##### earns it … he who doesn’t … pays it.”

– Albert Einstein

In finance the term “interest” is understood as the cost of borrowing money.

Interest exists as one of two types – simple or compound.  Whether interest is said to be simple or compound depends on how the interest is calculated.

In this article, we are going to look at the basics of compound interest. Knowing the basics of compound interest will help you make more informed decisions when borrowing or investing money.

### Compounding Interest Terms

I’ll be introducing several terms in our discussion so here are some quick definitions

Principal – the original amount borrowed or invested

Interest rate– the percentage rate that is calculated for the amount that accrues on a principal over a period of time

Compounding period – the number of periods in which the interest compounds – for example, monthly, yearly or continuously.

### What Is Compound Interest?

Compound interest is interest that is calculated both on the principal amount invested or borrowed and the accumulated interest over a previously defined period of time.

Because compound interest is the total of the principal and accumulated interest it is sometimes known as “interest on interest”.

It is the compounding effect of the interest that makes the difference in how much extra you must pay on a loan or the return you get from an investment.

– Warren Buffett

### How to Calculate Compound Interest

To calculate compound interest, you can use the formula

Compound interest = the total amount of the Principal plus the interest rate multiplied by the compounding period minus the principal at present

Or as an expression

P[1+i)n -1]

Where P=Principal, i=annual interest rate and n=the number of compounding periods. The “`1” is equivalent to P or the principal.

Looks complicated, doesn’t it?

Let’s look at an example that uses simpler math yet illustrates the basic concept of compounding.

### Compound Interest Basics – A Simple Example

In this example we are going to assume the following

• A deposit of \$100 into a bank account
• An interest rate of 10%
• An annual compounding period

In the real world interest calculations are much more complex – for example most banks use continuous compounding rather than simple annual or monthly compounding.

I am purposely simplifying things to illustrate the basics of compounding interest.

So we have deposited our \$100 at an annual interest rate of 10%. At the end of a years’ time we will – assuming we leave the money in the bank – have \$100 plus our 10% interest, or \$110

100 + 10% = 110

If we leave the money in the bank we will now accrue interest on our interest.

In other words, our principal is now \$110. So, will gain another 10% on the \$110.

110 + 10% = 121

So, we now have \$121 dollars because our interest compounded.

The same would hold true if our example was for a loan of \$100 with a two-year period and an annual interest rate of 10%

At the end of the two-year period we would have to pay back \$121 dollars to satisfy the terms of the loan.

### The power of Compounding Interest

Would you rather be given a million dollars in a month or have a penny double every day for a month? I know when I first heard this I knew there was something up. It was in my 8th grade math class and although this rate of return is very unlikely I learned a valuable lesson. So, to end let’s look at which option is best. A penny doubled every day would look something like this.

Day 1: \$.01
Day 2: \$.02
Day 3: \$.04
Day 4: \$.08
Day 5: \$.16
Day 6: \$.32
Day 7: \$.64
Day 8: \$1.28
Day 9: \$2.56
Day 10: \$5.12
Day 11: \$10.24
Day 12: \$20.48
Day 13: \$40.96
Day 14: \$81.92
Day 15: \$163.84

Ok, halfway there and things start to get interesting. At this point it still seems like a million dollars is the best deal. You’ll see shortly why all your elders have advised you to invest early and often because time is money and the more time your money has to work for you the better. The ending years will provide the greatest returns.

Day 16: \$327.68
Day 17: \$655.36
Day 18: \$1,310.72
Day 19: \$2,621.44
Day 20: \$5,242.88
Day 21: \$10,485.76
Day 22: \$20,971.52
Day 23: \$41,943.04
Day 24: \$83,886.08
Day 25: \$167,772.16
Day 26: \$335,544.32
Day 27: \$671,088.64
Day 28: \$1,342,177.28
Day 29: \$2,684,354.56
Day 30: \$5,368,709.12

Even if the month was February you would still come out ahead with the penny option. Comment below with your thoughts.

Check it out for yourself using the below compound interest calculator. Take some time and see how your investments or debts are compounding.