Title: Compound Interest
Course: Technical Math for Industry > Section: Module 6.0 Finance & Simple and Compound Interest

Compound Interest

But the bank says "If you paid me everything back after one year, and then I loaned it to you again ... I would be loaning you $1,100 for the second year!"

And Alex would pay $110 interest in the second year, not just $100.

Because Alex is paying 10% on $1,100 not just $1,000

This may seem unfair ... but imagine YOU were lending the money to Alex. After a year you think "Alex owes me $1,100 now, and is still using my money, I should get more interest!"

And so this is the normal way of calculating interest. It is called compounding.

With compounding we work out the interest for the first period, add it the total, and then calculate the interest for the next period, and so on ..., like this:

It is like paying interest on interest: after a year Alex owed $100 interest, the Bank thinks of that as another loan and charges interest on it, too.

After a few years it can get really large. This is what happens on a 5 Year Loan:

Year | Loan at Start | Interest | Loan at End
0 (Now) | $1,000.00 | ($1,000.00 × 10% = ) $100.00 | $1,100.00
1 | $1,100.00 | ($1,100.00 × 10% = ) $110.00 | $1,210.00
2 | $1,210.00 | ($1,210.00 × 10% = ) $121.00 | $1,331.00
3 | $1,331.00 | ($1,331.00 × 10% = ) $133.10 | $1,464.10
4 | $1,464.10 | ($1,464.10 × 10% = ) $146.41 | $1,610.51
5 | $1,610.51 |  |

So, after 5 Years Alex would have to pay back $1,610.51

And the Interest for the last year was $146.41 ... it sure grew quickly!

(Compare that to the Simple Interest of only $100 each year)

What is Year 0?

Year 0 is the year that starts with the "Birth" of the Loan, and ends just before the 1st Birthday.

Just like when a baby is born its age is zero, and will not be 1 year old until the first birthday.

So the start of Year 1 is the "1st Birthday". And we can know the start of Year 5 is exactly when the loan is 5 Years Old.

In Summary:

To calculate compound interest, work out the interest for the first period, add it on, and then calculate the interest for the next period, etc.

(There are quicker methods, see Compound Interest)

Why Borrow?

Well ... you may want to buy something you like. Paying it back will end up costing you more though.

But a business may be able to use the money to make even more money.

Example: Chicken Business

You borrow $1,000 to start a chicken business (to buy chicks, chicken food and so on).

A year later you sell the grown chickens for $1,200.

You pay back the bank $1,100 (the original $1,000 plus 10% interest) and you are left with $100 profit.

And you used someone else's money to do it!

But ... be careful. What if you only sold the chickens for $800? ... you would still have to pay the bank $1,100 and would face a $300 loss.

Investment

Compound Interest can work for you!

Investment is where you put money so it could grow, such as a bank, or a business.

If you invest your money at a good interest rate it can grow very nicely.

This is what 15% interest on $1,000 can do:

Year | Loan at Start | Interest | Loan at End
0 (Now) | $1,000.00 | ($1,000.00 × 15% = ) $150.00 | $1,150.00
1 | $1,150.00 | ($1,150.00 × 15% = ) $172.50 | $1,322.50
2 | $1,322.50 | ($1,322.50 × 15% = ) $198.38 | $1,520.88
3 | $1,520.88 | ($1,520.88 × 15% = ) $228.13 | $1,749.01
4 | $1,749.01 | ($1,749.01 × 15% = ) $262.35 | $2,011.36
5 | $2,011.36 |  |

It more than doubles in 5 Years!

An investment at 15% is not likely to be safe (see Investing introduction) ... but it does show you the power of compounding.

The graph of that investment looks like this:

Maybe you don't have $1,000? Here is what saving $200 every year for 10 Years at 10% interest can do:

$3,506.23 after 10 Years!
For 10 Years of $200 each year.

Less Than One Year ...

Interest is not always charged yearly. It can be charged Semi-annually (every 6 months), Monthly, even Daily!

But the same rules apply:

- If it is simple interest, just work out the interest for one period, and multiply by the number of periods.
- If it is compound interest, work out the interest for the first period, add it on and then calculate the interest for the next period, etc.