# Basic interest

People loan money to other people all the time.  To buy a house, you usually have to take out a home loan from the bank.  The bank will lend you the money to pay for the house.  Same for a car.  So what’s the catch?

Well, it’s called interest.  A bank isn’t going to lend you money to be nice.  They’re interested in earning money, and they can do it by loaning money to you.  How they do it is by charging interest on the amount of money they loan to you.  Now obviously, you eventually have to pay back the money that the bank lent you.  But you also have to pay back interest as well.

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There are lots of types of interest.  The easiest one to work with is simple interest.

## Simple Interest

To work with simple interest, we need to learn a few financial terms.

### Principal

Note this is the principal, not the principle (which is a rule or law).  The principal is the amount of money that has been lent or borrowed.

### Interest rate

The interest rate tells you what percentage of the amount borrowed (the principal) needs to be paid at regular time intervals.  Often the time interval is a year – so you pay back interest once a year.

### Term length

The term length is how long the person who has borrowed the money has to pay interest for.

### Per annum

This just means, “per year.”

### The simple interest formula

You use this to work out how much interest needs to be payed, if you know the principal, the interest rate, and the term length.

Here’s the formula:

Only one important thing to remember with this formula.  The units of time you used for the interest rate and the term length have to be the same.  So, say I have an interest rate of 5% every six months.  I would have to write down the term length in terms of blocks of six months.  So if the term length was one year, I’d write it down in the formula as ‘2’ – since there are two six month blocks in one year.

 Jason has borrowed \$4000 from the bank to help pay for a new car.  The bank loaned him the \$4000 at an interest rate of 7% per annum, with an 18 month term.  How much interest will he have to pay back to the bank over the 18 months?  How much money in total will he end up paying back to the bank? Solution So there are two parts to the question.  One part is to work out how much interest he’ll have to pay over the 18 months.  The other is to work out the total amount he has to pay back.  Let’s calculate the interest first. We get to use the simple interest formula:                    The principal is just the size of the loan - \$4000.  The interest rate is 7% per year.  The important thing to remember here is that since the interest rate is per year, we must use the same unit of time (years) when we write down our term length.  In the question, it says the term length is 18 months.  Well, how many years is 18 months?  It’s 1.5 years.  So our term length is 1.5 years:                                         So now for the second part of the question, which is working out the total amount he will have to pay back.  We know that he has to pay back the actual amount he borrowed (the principal), as well as the interest:

 A common question with simple interest asks how long it will take to earn a certain amount of interest, if you’re given the interest rate and the amount of money invested.  For example, one might want to know how long it would take to earn \$500 interest on an investment amount of \$3500 at an interest rate of 8% per annum. Solution The thing we’re interested in finding is how long – a time period.  The only time period in our simple interest formula is the term length.  What we need to do is rearrange this equation so that it’s in the form “term length = something…”:                         Now we know how much simple interest we want paid - \$500.  We know that the principal is \$3500.  We know that the interest rate is 8%.  All we need to do is plug this into the equation, not forgetting to convert the interest rate percentage into a decimal:                                              So we will need 1.786 term lengths to earn this much simple interest, assuming that we can get the interest paid out to us at any time, instead of just at the end of each term.  If we can only get the interest paid to us at the end of a term, then we’ll need 2 term lengths, since after 1 term we won’t have made \$500 interest yet. Now how long is a term?  Our interest rate was given to us per annum, so our term must be a year.  So 1.786 terms is going to be: