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

Interest: how much is paid for the use of money (as a percent, or an amount)

Money is Not Free to Borrow

People can always find a use for money, so it costs to borrow money.

How Much does it Cost to Borrow Money?

Different places charge different amounts at different times!

But they usually charge this way:

 | As a percent (per year) of the amount borrowed |
It is called Interest

Example: Borrow $1,000 from the Bank
Alex wants to borrow $1,000. The local bank says "10% Interest". So to borrow the $1,000 for 1 year will cost:

$1,000 × 10% = $100

In this case the "Interest" is $100, and the "Interest Rate" is 10% (but people often say "10% Interest" without saying "Rate")

Of course, Alex will have to pay back the original $1,000 after one year, so this is what happens:

Alex Borrows $1,000, but has to pay back $1,100

This is the idea of Interest ... paying for the use of the money.

 | Note: I am showing a full year loan, but banks often want you to pay back the loan in small monthly amounts, and they also charge extra fees too!

Words

There are special words used when borrowing money, as shown here:

Alex is the Borrower, the Bank is the Lender

The Principal of the Loan is $1,000

The Interest is $100

The important part of the word "Interest" is Inter- meaning between (you seeinter- in words like interior and interval), because the interest happens between the start and end of the loan.

More Than One Year ...

What if Alex wanted to borrow the money for 2 Years?

Simple Interest

If the bank charges "Simple Interest" then Alex just pays another 10% for the extra year.

Alex pays Interest of ($1,000 × 10%) x 2 Years = $200

That is how simple interest works ... pay the same amount of interest every year.

Example: Alex borrows $1,000 for 5 Years, at 10% simple interest:

• Interest = $1,000 × 10% x 5 Years = $500
• Plus the Principal of $1,000 means Alex needs to pay $1,500 after 5 Years

There is a formula for simple interest

I = Prt

where

- I = interest
- P = amount borrowed (called "Principal")
- r = interest rate
- t = time

Like this:

Example: Jan borrowed $3,000 for 4 Years at 5% interest rate, how much interest is that?

I = | Prt
I = | $3,000 × 5% × 4 years
I = | 3000 × 0.05 × 4
I = | $600