{"id":1153,"date":"2018-04-29T11:02:33","date_gmt":"2018-04-29T18:02:33","guid":{"rendered":"https:\/\/financer.com\/?page_id=1153"},"modified":"2024-12-10T21:35:24","modified_gmt":"2024-12-11T05:35:24","slug":"effective-interest-rate","status":"publish","type":"wiki","link":"https:\/\/financer.com\/loans\/articles\/effective-interest-rate\/","title":{"rendered":"Effective Interest Rate"},"content":{"rendered":"\n

When you take out a loan, whether it\u2019s a personal loan<\/a>, payday loan<\/a>, mortgage<\/a>, or auto loan<\/a>, you will see various interest rates, including the stated interest rate and annual percentage rate. <\/p>\n\n\n\n

You seldom see the Effective Annual<\/strong> Interest Rate<\/strong> (EAR), despite its importance.<\/p>\n\n\n\n

The effective annual interest rate may also be referred to using other terms such as the effective interest rate (EIR), annual equivalent rate (AER), or effective rate.<\/p>\n\n\n\n

So, what is the effective interest rate and how does it work? <\/p>\n\n\n\n

How the Effective Interest Rate Works<\/h2>\n\n\n\n

The effective interest rate is the total interest cost associated with a loan<\/strong>. <\/p>\n\n\n\n

All loans have compound interest<\/a>, meaning the bank adds the previous month\u2019s accrued interest to the principal when calculating your future interest payments<\/a>. <\/p>\n\n\n\n

The effective rate takes this into consideration and expresses it as a rate that is generally slightly higher than the stated interest rate but lower than the APR.<\/p>\n\n\n\n

How to Calculate Effective Interest Rate<\/h2>\n\n\n\n

The effective rate of interest<\/a> is one of the easier financial calculations to make, but you still need an in-depth equation to figure it out. <\/p>\n\n\n\n

The effective interest rate formula is: <\/p>\n\n\n\n

r = (1 + i\/n)^n \u2013 1<\/strong><\/p>\n\n\n\n

The \u201cr\u201d is your effective interest rate, \u201ci\u201d is the stated interest rate in its decimal format (3% is 0.03), and \u201cn\u201d is the number of times the interest compounds in a year. <\/p>\n\n\n\n

Generally, the \u201cn\u201d will be a 12 because most loans compound monthly, but, in some rare cases, it may also be daily, weekly, or continuously.<\/p>\n\n\n\n

An example:<\/strong><\/p>\n\n\n\n

Let\u2019s say you have a $100,000 loan with a 3% stated interest rate that compounds monthly, here is how to calculate the effective interest rate: <\/p>\n\n\n\n

r = (1 + 0.03\/12)^12 \u2013 1<\/p>\n\n\n\n

In this case the 3% stated interest rate is equal to a 3.04% effective interest rate.<\/p>\n\n\n\n

While the difference may seem insignificant, this can be a helpful tool when comparing loan offers that are offering virtually identical terms.<\/p>\n\n\n\n

The table below shows how effective annual rates change with compounding:<\/p>\n\n\n\n

Interest Rate<\/th>Semi-Annual<\/th>Quarterly<\/th>Monthly<\/th>Daily<\/th><\/tr><\/thead>
1%<\/td>1.0025%<\/td>1.0038%<\/td>1.0046%<\/td>1.0050%<\/td><\/tr>
2%<\/td>2.0100%<\/td>2.0151%<\/td>2.0184%<\/td>2.0201%<\/td><\/tr>
3.%<\/td>3.0225%<\/td>3.0339%<\/td>3.0416%<\/td>3.0453%<\/td><\/tr>
4%<\/td>4.0400%<\/td>4.0604%<\/td>4.0742%<\/td>4.0808%<\/td><\/tr>
5%<\/td>5.0625%<\/td>5.0945%<\/td>5.1162%<\/td>5.1267%<\/td><\/tr>
10%<\/td>10.2500%<\/td>10.3813%<\/td>10.4713%<\/td>10.5156%<\/td><\/tr>
15%<\/td>15.5625%<\/td>15.8650%<\/td>16.0755%<\/td>16.1798%<\/td><\/tr>
20%<\/td>21.0000%<\/td>21.5506%<\/td>21.9391%<\/td>22.1336%<\/td><\/tr>
25%<\/td>26.5625%<\/td>27.4429%<\/td>28.0732%<\/td>28.3916%<\/td><\/tr>
30%<\/td>32.2500%<\/td>33.5469%<\/td>34.4889%<\/td>34.9692%<\/td><\/tr>
35%<\/td>38.0625%<\/td>39.8676%<\/td>41.1980%<\/td>41.8830%<\/td><\/tr>
40%<\/td>44.0000%<\/td>46.4100%<\/td>48.2126%<\/td>49.1498%<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n\t\t

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Why the Effective Rate is Important<\/h2>\n\n\n\n

The effective rate of interest determines an investment’s true return<\/strong> or a loan’s true interest rate<\/strong>.<\/p>\n\n\n\n

The annual interest rate and effective interest rate can differ significantly due to compounding. The effective rate can help you figure out the best loan rate or which investment<\/a> offers the best return.<\/p>\n\n\n\n

When compounding is taken into consideration, the EAR will always be higher<\/strong> than the stated annual interest rate.<\/p>\n\n\n\n

As an example, if you deposit $10,000 into a savings account with a stated interest rate of 12%, compounding monthly, the effective rate will be around 12.68%, as the following table shows:<\/p>\n\n\n\n

Month<\/th>Balance<\/th>Interest Earned<\/th>Ending Balance<\/th><\/tr><\/thead>
1<\/td>$10,000.00<\/td>$100<\/td>$10,100.00<\/td><\/tr>
2<\/td>$10,100.00<\/td>$101.00<\/td>$10,201.00<\/td><\/tr>
3<\/td>$10,201.00<\/td>$102.01<\/td>$10,303.01<\/td><\/tr>
4<\/td>$10,303.01<\/td>$103.03<\/td>$10,406.04<\/td><\/tr>
5<\/td>$10,406.04<\/td>$104.06<\/td>$10,510.10<\/td><\/tr>
6<\/td>$10,510.10<\/td>$105.10<\/td>$10,615.20<\/td><\/tr>
7<\/td>$10,615.20<\/td>$106.15<\/td>$10,721.35<\/td><\/tr>
8<\/td>$10,721.35<\/td>$107.21<\/td>$10,828.56<\/td><\/tr>
9<\/td>$10,828.56<\/td>$108.29<\/td>$10,936.85<\/td><\/tr>
10<\/td>$10,936.85<\/td>$109.73<\/td>$11,046.22<\/td><\/tr>
11<\/td>$11,046.22<\/td>$110.46<\/td>$11,156.68<\/td><\/tr>
12<\/td>$11,156.68<\/td>$111.57<\/td>$11,268.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

The change in account balance from the start at $10,000, to the end where the balance is $11,268.25, equals an effective interest rate (12.6825%).<\/p>\n\n\n\n

Even though the bank stated a 12% interest rate, your investment grew by 12.68%.<\/p>\n","protected":false},"author":11463,"featured_media":84675,"comment_status":"open","ping_status":"closed","template":"","meta":{"disable_branded_featured_image":false,"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","ep_exclude_from_search":false,"footnotes":""},"categories":[1076],"_links":{"self":[{"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/wiki\/1153"}],"collection":[{"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/types\/wiki"}],"author":[{"embeddable":true,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/users\/11463"}],"replies":[{"embeddable":true,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/comments?post=1153"}],"version-history":[{"count":46,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/wiki\/1153\/revisions"}],"predecessor-version":[{"id":51610,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/wiki\/1153\/revisions\/51610"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/media\/84675"}],"wp:attachment":[{"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/media?parent=1153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/financer.com\/wp-json\/wp\/v2\/categories?post=1153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}