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392 lines
19 KiB
HTML
392 lines
19 KiB
HTML
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<head>
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<title>Introduction to Interest</title>
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<meta name="description" content="Interest: how much is paid for the use of money (as a percent, or an amount)" />
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Interest <i>(An Introduction)</i></h1>
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<p align="center"><i>Interest: how much is paid for the use of money (as a percent, or an amount)</i></p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/coin-stack.jpg" width="75" height="100" alt="coin stack" /></p>
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<h2>Money is Not Free to Borrow</h2>
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<p>People can always find a use for money, so it <b>costs to borrow money</b>.</p>
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<h2>How Much does it Cost to Borrow Money?</h2>
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<p> Different places charge different amounts at different times! </p>
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<p>But they usually charge this way:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<td class="larger"><img src="../images/style/percent.gif" width="41" height="44" alt="percent" /></td>
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<td class="larger">
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<h3 align="center">As a percent (per year) of the amount borrowed</h3> </td>
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<td class="larger"><img src="../images/style/percent.gif" width="41" height="44" alt="percent" /></td>
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</tr>
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<tr>
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<td class="larger" colspan="3">
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<div align="center"><br />
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It is called <b>Interest<br />
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</b></div> </td>
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</tr>
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</table>
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</div>
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<p><br />
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</p>
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<div class="example">
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<h3>Example: Borrow $1,000 from the Bank</h3>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/bank.jpg" width="100" height="77" alt="bank" /></p>
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<p>Alex wants to borrow $1,000. The local bank says "<i><b>10% Interest</b></i>". So to borrow the $1,000 for 1 year will cost:</p>
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<p align="center"><b>$1,000 × 10% = $100</b></p>
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</div>
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<p> In this case the "Interest" is $100, and the "Interest Rate" is 10% (but people often say "10% Interest" without saying "Rate")</p>
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<p>Of course, Alex will have to pay back the original $1,000 after one year, so this is what happens:</p>
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<table border="0" align="center">
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<tr>
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<td><img src="images/interest1.svg" alt="today Alex gets $1000, next year Alex pays back $1000 plus $100 interest" style="max-width:100%" /></td>
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<td rowspan="2" valign="bottom"><img src="images/coin-stack-add.jpg" width="106" height="140" alt="coin stack add" /></td>
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</tr>
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<tr>
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<td><b>Alex Borrows $1,000, but has to pay back $1,100</b></td>
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</tr>
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</table>
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<h3 align="center">This is the idea of Interest ... paying for the use of the money.</h3>
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<br />
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<table border="0" align="center">
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<tr>
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<td><img src="../images/style/pencil-paper.gif" width="39" height="35" alt="pencil paper" /></td>
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<td>
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<i>Note: This example is a simple full year loan, but banks often want the loan paid back in monthly amounts, and they also charge extra fees too!</i></td>
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</tr>
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</table>
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<h2>Words</h2>
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<p>There are special words used when borrowing money, as shown here:</p>
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<p align="center"><img src="images/loan-words.svg" alt="loan words" style="max-width:100%" /></p>
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<p align="center">Alex is the <b>Borrower</b>, the Bank is the <b>Lender</b></p>
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<p align="center">The <b>Principal</b> of the Loan is $1,000 </p>
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<p align="center">The <b>Interest</b> is $100</p>
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<div class="words">The important part of the word "Interest" is <i>Inter-</i> meaning <i>between</i> (we see <i>inter-</i> in words like <i>interior</i> and <i>interval</i>), because the interest happens between the start and end of the loan. </div>
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<h2>More Than One Year ...</h2>
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<p>What if Alex wanted to borrow the money for 2 Years?</p>
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<h3>Simple Interest</h3>
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<p>If the bank charges "Simple Interest" then Alex just pays another 10% for the extra year.</p>
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<p align="center"><img src="images/interest2s.svg" alt="today Alex gets $1000, in 2 years Alex pays back $1000 plus $200 interest" style="max-width:100%" /><br>
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Alex pays Interest of ($1,000 × 10%) x 2 Years = $200</p>
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<p>That is how simple interest works ... pay the same amount of interest every year.</p>
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<div class="example">
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<h3>Example: Alex borrows $1,000 for 5 Years, at 10% simple interest: </h3>
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<p>• Interest = $1,000 × 10% x 5 Years = $500<br />
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• Plus the Principal of $1,000 means Alex needs to pay $1,500 after 5 Years</p>
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</div>
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<div class="example">
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<h3>Example: Alex borrows $1,000 for 7 Years, at 6% simple interest: </h3>
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<p>• Interest = $1,000 × 6% x 7 Years = $420<br />
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• Plus the Principal of $1,000 means Alex needs to pay $1,420 after 7 Years</p>
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</div>
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<p>There is a formula for simple interest</p>
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<div class="def">
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<p align="center" class="large">I = Prt</p>
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<p>where </p>
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<ul>
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<li>I = interest</li>
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<li>P = amount borrowed (called "Principal")</li>
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<li>r = interest rate</li>
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<li>t = time</li>
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</ul>
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</div>
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<p>Like this:
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</p>
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<div class="example">
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<h3>Example: Jan borrowed $3,000 for 4 Years at 5% interest rate, how much interest is that? </h3>
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<table border="0" align="center">
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<tr>
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<td>I = </td>
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<td>Prt</td>
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</tr>
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<tr>
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<td>I = </td>
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<td>$3,000 × 5% × 4 years </td>
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</tr>
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<tr>
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<td>I = </td>
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<td>$3000 × 0.05 × 4 </td>
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</tr>
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<tr>
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<td>I = </td>
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<td><span class="larger">$600</span></td>
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</tr>
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</table>
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</div>
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<p>But banks almost NEVER charge simple interest, they prefer Compound Interest:</p>
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<h3>Compound Interest</h3>
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<p>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 <b>$1,100 for the second year</b>!" so I want more interest:</p>
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<p align="center"><img src="images/interest2c.svg" alt="today Alex gets $1000, next year $1100, 2nd year Alex pays back $1000 plus ($100+$110) interest" style="max-width:100%" /></p>
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<p align="center">And Alex pays <b>$110</b> interest in the second year, not just $100.</p>
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<p align="center"><b>Because Alex is paying 10% on $1,100 not just $1,000</b></p>
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<p class="indent50px">This may seem unfair ... but imagine YOU lend the money to Alex. After a year you think <i>"Alex owes me $1,100 now, and is still using my money, I should get more interest!"</i></p>
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<p>And so this is the normal way of calculating interest. It is called <b>compounding</b>.</p>
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<p>With <b>compounding </b>we work out the interest for the first period, add it the total, and <b>then</b> calculate the interest for the next period, and so on ..., like this:</p>
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<p align="center"><img src="images/interest-compound-flow.svg" alt="interest compound $1000, 10%=$100, $1100, 10%=$110, $1210, 10%=$121, etc " style="max-width:100%" /></p>
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<p>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.</p>
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<p>After a few years it can get really large. This is what happens on a 5 Year Loan:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<th width="90">
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<div align="center">Year</div> </th>
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<th width="110">
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<div align="center">Loan at Start</div> </th>
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<th width="270">
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<div align="center">Interest</div> </th>
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<th width="110">
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<div align="center">Loan at End</div> </th>
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</tr>
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<tr>
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<td>
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<div align="center">0 (Now)</div> </td>
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<td>
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<div align="center">$1,000.00</div> </td>
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<td>
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<div align="center">($1,000.00 × 10% = ) <b>$100.00</b></div> </td>
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<td>
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<div align="center">$1,100.00</div> </td>
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</tr>
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<tr>
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<td>
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<div align="center">1</div> </td>
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<td>
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<div align="center">$1,100.00</div> </td>
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<td>
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<div align="center">($1,100.00 × 10% = ) <b>$110.00</b></div> </td>
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<td>
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<div align="center">$1,210.00</div> </td>
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</tr>
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<tr>
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<td>
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<div align="center">2</div> </td>
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<td>
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<div align="center">$1,210.00</div> </td>
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<td>
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<div align="center">($1,210.00 × 10% = ) <b>$121.00</b></div> </td>
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<td>
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<div align="center">$1,331.00</div> </td>
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</tr>
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<tr>
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<td>
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<div align="center">3</div> </td>
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<td>
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<div align="center">$1,331.00</div> </td>
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<td>
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<div align="center">($1,331.00 × 10% = ) <b>$133.10</b></div> </td>
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<td>
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<div align="center">$1,464.10</div> </td>
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</tr>
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<tr>
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<td>
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<div align="center">4</div> </td>
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<td>
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<div align="center">$1,464.10</div> </td>
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<td>
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<div align="center">($1,464.10 × 10% = ) <b>$146.41</b></div> </td>
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<td>
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<div align="center">$1,610.51</div> </td>
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</tr>
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<tr>
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<td>
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<div align="center">5</div> </td>
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<td>
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<div align="center">$1,610.51</div> </td>
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<td>
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<div align="center"></div> </td>
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<td>
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<div align="center"></div> </td>
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</tr>
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</table>
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</div>
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<p align="center">So, after 5 Years Alex has to pay back <b>$1,610.51</b></p>
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<p align="center"><b>And the Interest for the last year was $146.41 ... it sure grew quickly!</b></p>
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<p align="center"><i>(Compare that to the Simple Interest of only $100 each year)</i></p>
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<h3>What is Year 0? </h3>
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<p><b>Year 0</b> is the year that starts with the "Birth" of the Loan, and ends just before the 1st Birthday. </p>
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<p align="left" class="center80">Just like when a baby is born its age is <b>zero</b>, and will not be 1 year old until the first birthday. </p>
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<div></div>
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<p>So the start of <b>Year 1</b> is the "1st Birthday". And the <b>start of Year 5</b> is exactly when the loan is 5 years old.</p>
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<div class="center80">
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<p><b><span class="larger">In Summary: </span></b></p>
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<p><span class="larger">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. </span></p>
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<p>(There are quicker methods, see <a href="compound-interest.html">Compound Interest</a>)</p>
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</div>
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<h2>Why Borrow?</h2>
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<p>Well ... you may want to buy something you like. Paying it back will end up costing you more though.</p>
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<p>But a business may be able to use the money to make <b>even more</b> money.</p>
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<div class="example"><img src="images/chicks.jpg" width="100" height="100" style="float:left; margin: 10px;" alt="chicks" />
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<h3>Example: Chicken Business</h3>
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<p>You borrow $1,000 to start a chicken business (to buy chicks, chicken food and so on). </p>
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<p>A year later you sell all the grown chickens for $1,200. </p>
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<p>You pay back the bank $1,100 (the original $1,000 plus 10% interest) and you are left with <b>$100 profit</b>.</p>
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<p align="center"><b><i>And you used someone else's money to do it!</i></b></p>
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<p>But be careful! What if you only sold the chickens for $800? ... the bank still wants $1,100 and you end up with a <b>$300 loss.</b></p>
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</div>
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<h2>Investment</h2>
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<p>Compound Interest can <b>work for you</b>! </p>
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<p><b>Investment</b> is when you put money where it <b>can grow</b>, such as a bank, or a business.</p>
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<p>If you invest your money at a good interest rate it can grow very nicely.</p>
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<p>This is what 15% interest on $1,000 can do:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<th width="90">
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<div align="center">Year</div> </th>
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<th width="110">
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<div align="center">Loan at Start</div> </th>
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<th width="270">
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<div align="center">Interest</div> </th>
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<th width="110">
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<div align="center">Loan at End</div> </th>
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</tr> <tr>
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<td>
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<div align="center">0 (Now)</div> </td>
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<td>
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||
<div align="center">$1,000.00</div> </td>
|
||
<td>
|
||
<div align="center">($1,000.00 × 15% = ) <b>$150.00</b></div> </td>
|
||
<td>
|
||
<div align="center">$1,150.00</div> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<div align="center">1</div> </td>
|
||
<td>
|
||
<div align="center">$1,150.00</div> </td>
|
||
<td>
|
||
<div align="center">($1,150.00 × 15% = ) <b>$172.50</b></div> </td>
|
||
<td>
|
||
<div align="center">$1,322.50</div> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<div align="center">2</div> </td>
|
||
<td>
|
||
<div align="center">$1,322.50</div> </td>
|
||
<td>
|
||
<div align="center">($1,322.50 × 15% = ) <b>$198.38</b></div> </td>
|
||
<td>
|
||
<div align="center">$1,520.88</div> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<div align="center">3</div> </td>
|
||
<td>
|
||
<div align="center">$1,520.88</div> </td>
|
||
<td>
|
||
<div align="center">($1,520.88 × 15% = ) <b>$228.13</b></div> </td>
|
||
<td>
|
||
<div align="center">$1,749.01</div> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<div align="center">4</div> </td>
|
||
<td>
|
||
<div align="center">$1,749.01</div> </td>
|
||
<td>
|
||
<div align="center">($1,749.01 × 15% = ) <b>$262.35</b></div> </td>
|
||
<td>
|
||
<div align="center">$2,011.36</div> </td>
|
||
</tr>
|
||
<tr>
|
||
<td>
|
||
<div align="center">5</div> </td>
|
||
<td>
|
||
<div align="center">$2,011.36</div> </td>
|
||
<td>
|
||
<div align="center"></div> </td>
|
||
<td>
|
||
<div align="center"></div> </td>
|
||
</tr>
|
||
</table></div>
|
||
<p align="center"><b>It more than doubles in 5 Years!</b></p>
|
||
<p>An investment at 15% is not likely to be safe (see <a href="investing-introduction.html">Investing introduction</a>) ... but it does show us the power of compounding.</p>
|
||
<p> The graph of that investment looks like this:</p>
|
||
|
||
<p align="center"><img src="images/interest2c-graph.gif" width="382" height="252" alt="interest graph" /></p>
|
||
<p>Maybe you don't have $1,000? Here is what saving $200 every year for 10 Years at 10% interest can do:</p>
|
||
<p align="center"><img src="images/interest2c-graph2.gif" width="381" height="253" alt="interest graph" /></p>
|
||
<p align="center"><b>$3,506.23</b> after 10 Years!<br />
|
||
For 10 Years of $200 each year.</p>
|
||
<h2>Less Than One Year ...</h2>
|
||
<p>Interest is not always charged yearly. It can be charged Semi-annually (every 6 months), Monthly, even Daily!</p>
|
||
<p>But the same rules apply:</p>
|
||
<ul>
|
||
<li>For simple interest: work out the interest for one period, and multiply by the number of periods. </li>
|
||
<li>For compound interest: work out the interest for the first period, add it on and then calculate the interest for the next period, etc.</li>
|
||
</ul>
|
||
<p> </p>
|
||
<div class="questions">
|
||
<script type="text/javascript">getQ(1702, 1703, 1704, 1705, 3749, 3750, 3751, 1706, 1707, 1708);</script>
|
||
</div>
|
||
|
||
<div class="related"><a href="compound-interest.html">Compound Interest</a>
|
||
<a href="investment-graph.html">Investment Graph</a></div>
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