{"id":3540,"date":"2018-05-02T23:59:07","date_gmt":"2018-05-02T18:29:07","guid":{"rendered":"https:\/\/www.antworksmoney.com\/blog\/?page_id=3540"},"modified":"2019-09-25T12:28:45","modified_gmt":"2019-09-25T06:58:45","slug":"compound-interest-formula","status":"publish","type":"post","link":"https:\/\/www.antworksmoney.com\/blog\/compound-interest-formula\/","title":{"rendered":"Compound Interest Formula"},"content":{"rendered":"<p>Compound interest is a useful financial concept in which your interest earned is added to your principal. This amount then continues to earn more interest. So in this case, you also earn interest on the interest you\u2019ve already earned. So your balance grows at an increasing rate. In a sense, you reinvest your interest, rather than receiving a pay-out.<\/p>\n<ul>\n<li>Year 1 &#8211; You earn interest on your Principal.<\/li>\n<li>Year 2 &#8211; You earn interest on your (Principal + Interest of Year 1).<\/li>\n<li>Year 3 &#8211; You earn interest on your (Principal + Interest of Year 1 + Interest of Year 2).<\/li>\n<\/ul>\n<h2>Types of Compound Interest<\/h2>\n<p>There are generally two types of compound interest used.<\/p>\n<ul>\n<li><strong>Periodic Compounding &#8211;<\/strong>\u00a0Under this method, the interest rate is applied at intervals and generated. This interest is added to the principal. Periods here would mean annually, bi-annually, monthly, or weekly.<\/li>\n<\/ul>\n<ul>\n<li><strong>Continuous Compounding\u00a0<\/strong>&#8211; This method uses a natural log-based formula and calculates interest at the smallest possible interval. This interest is added back to the principal. This can be equalled to the constant rate of growth for all natural growth. This figure was born out of physics. It uses Euler\u2019s number which is a famous irrational number which is known to more than 1 trillion digits of accuracy. Euler\u2019s number is denominated by the letter \u201cE\u201d.<\/li>\n<\/ul>\n<h2>Periodic Compound Interest Formula Overview<\/h2>\n<p>There are two formulas you can use to calculate compound interest, depending on what result you wish to find out. You can find out the following:<\/p>\n<ul>\n<li>The total value of the deposit.<\/li>\n<li>The total compound interest earned.<\/li>\n<\/ul>\n<h3>Value of the Deposit<\/h3>\n<p>Formulas can be a deterrent to many. If you aren\u2019t savvy with math, your eyes turn away from these codes or just skip them altogether. But once it\u2019s explained, it\u2019s pretty simple to understand. To calculate the total value of your deposit, the formula is as follows:<\/p>\n<p><strong>P (1+ i\/n)<sup>nt<\/sup><\/strong><\/p>\n<p>P = Principal invested.<\/p>\n<p>i = Nominal Rate of Interest.<\/p>\n<p>n = Compounding Frequency or number of compounding periods in a year.<\/p>\n<p>t = Time, meaning the length of time the interest is applicable, generally in years.<\/p>\n<p>Simply put, you calculate the interest rate divided by the number of times in a year the compound interest is generated. For instance, if your bank compounds interest quarterly, there are 4 quarters in a year, so n = 4. This result must be multiplied to the power of the deposit period. For example, if your deposit is for 10 years, t = 10. This whole result should be multiplied by the principal you invested. The result generated will equal the total accumulated value of your deposit. You can find out how much your deposit is worth currently after accumulating interest.<\/p>\n<h3>Total Compound Interest Earned<\/h3>\n<p>To find out how much interest was earned, you can use the following\u00a0<strong>formula for Compound Interest<\/strong>.<\/p>\n<p><strong>P[(1+ i\/n))<sup>nt<\/sup>-1]<\/strong><\/p>\n<h3>Compound Interest Equation and Calculation<\/h3>\n<p>To understand the compound interest equation further, we can break it down in simpler terms. If you decide to invest in a fixed deposit with compound interest, this is how you will earn interest every year.<\/p>\n<table class=\"table table-curved\">\n<tbody>\n<tr>\n<td><strong>Period<\/strong><\/td>\n<td><strong>Deposit Balance<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Investment<\/td>\n<td>P<\/td>\n<\/tr>\n<tr>\n<td>Year 1<\/td>\n<td>P + iP<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td>(P+ iP) + i(P+iP)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>To collapse this formula, we can pull out factors of (1+i). Simply substitute iP with (1+i) to get the following:<\/p>\n<table class=\"table table-curved\">\n<tbody>\n<tr>\n<td><strong>Period<\/strong><\/td>\n<td><strong>Deposit Balance<\/strong><\/td>\n<\/tr>\n<tr>\n<td>Investment<\/td>\n<td>P<\/td>\n<\/tr>\n<tr>\n<td>Year 1<\/td>\n<td>P(1+i)<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td>P(1+i)<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td>P(1+i)<sup>3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Formula for Annual Compound Interest<\/h2>\n<p>To calculate the compound interest for a number of years together, we need to multiply P(1+i) to the power of the number of years of the deposit. So we end up with this formula:<\/p>\n<p><strong>P (1+ i\/n)<sup>n<\/sup><\/strong><\/p>\n<p>This formula can be used to calculate compound interest that is compounded annually. This means you receive interest only once a year. It is added to your principal, and you continue to earn interest on the new amount.<\/p>\n<h2>Half-Yearly, Quarterly, Monthly Compound Interest Formula<\/h2>\n<p>If you are earning interest multiple times in a year, you need to factor in this number into the equation. So the formula generated is:<\/p>\n<p><strong>P (1+ i\/n)<sup>nt<\/sup><\/strong><\/p>\n<p>This formula can also be used for instances where the interest is compounded once every two years. In this case, n = 0.5, as each year is calculated as half.<\/p>\n<h2>The Benefit of Compound Interest<\/h2>\n<p>Compound interest is your biggest friend when it comes to deposits and investments. Working in favor of investments, you stand to gain much more from the interest payable. But compound interest will be your worst enemy when it is calculated on your loan or other debt. You will end up paying significantly more interest on your loan. The benefits of compound interest can be listed as follows:<\/p>\n<ul>\n<li><em><strong>Reinvestment &#8211;<\/strong><\/em>\u00a0The interest earned will be reinvested into the same deposit.<\/li>\n<li><em><strong>Higher value of the deposit &#8211;\u00a0<\/strong><\/em>Compound interest leads to a higher value of the deposit. Upon maturity, your deposit will be more than a deposit with simple interest.<\/li>\n<li><em><strong>Long-term savings &#8211;<\/strong><\/em>\u00a0Compound interest deposits encourage long-term savings as the return on investment is much higher after 10 years or more.<\/li>\n<li><em><strong>Increased Earnings &#8211;\u00a0<\/strong><\/em>Options of compounding monthly, quarterly, and half-yearly increase the interest earned.<\/li>\n<\/ul>\n<h2>Financial platforms where compound interest is applicable<\/h2>\n<p>Compound interest is used for both debit and credit aspects of the financial world. Listed below are some of the investments and credit options that use compound interest.<\/p>\n<p><strong>Investments<\/strong><\/p>\n<ul>\n<li>Savings Accounts<\/li>\n<li>Fixed Deposits<\/li>\n<li>Recurring Deposits<\/li>\n<li>Other Certificates of Deposits<\/li>\n<li>Reinvested Dividend Stocks<\/li>\n<li>Retirement Funds<\/li>\n<\/ul>\n<p><strong>Debt<\/strong><\/p>\n<ul>\n<li>Loans<\/li>\n<li>Credit Cards<\/li>\n<li>Mortgages<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Compound interest is a useful financial concept in which your interest earned is added to your principal. This amount then continues to earn more interest. So in this case, you also earn interest on the interest you\u2019ve already earned. So your balance grows at an increasing rate. In a sense, you reinvest your interest, rather &hellip; <a href=\"https:\/\/www.antworksmoney.com\/blog\/compound-interest-formula\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Compound Interest Formula&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-3540","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\r\n<title>Compound Interest Formula - Antworks Money<\/title>\r\n<meta name=\"description\" content=\"Compound interest is a useful financial concept in which your interest earned is added to your principal. 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