{"id":7340,"date":"2022-03-21T14:54:22","date_gmt":"2022-03-21T09:24:22","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7340"},"modified":"2026-01-29T06:04:34","modified_gmt":"2026-01-29T00:34:34","slug":"what-is-compound-interest","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-compound-interest\/","title":{"rendered":"What is compound interest?"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\"><a href=\"https:\/\/www.investopedia.com\/terms\/c\/compoundinterest.asp#:~:text=Compound%20interest%20(or%20compounding%20interest,accumulated%20interest%20from%20previous%20periods.\" target=\"_blank\" rel=\"noreferrer noopener\">Compound interest<\/a><\/h2>\n\n\n\n<p>In <a href=\"https:\/\/www.investopedia.com\/terms\/c\/compoundinterest.asp#:~:text=Compound%20interest%20(or%20compounding%20interest,accumulated%20interest%20from%20previous%20periods.\" target=\"_blank\" rel=\"noreferrer noopener\">compound interest<\/a>, the principal does not remain the same but increases at the end of each interest period. In other words, compound interest is calculated on interest as well as on principal.  Therefore, <a href=\"https:\/\/www.investopedia.com\/terms\/c\/compoundinterest.asp#:~:text=Compound%20interest%20(or%20compounding%20interest,accumulated%20interest%20from%20previous%20periods.\" target=\"_blank\" rel=\"noreferrer noopener\">compound interest <\/a>is sometimes described as \u2018interest on interest\u2019.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Some important definitions<\/strong><\/h2>\n\n\n\n<p><strong>Compound Interest \u2013 <\/strong>It is the difference between the compound amount and original principal amount. so that we can find the compound interest by using the formula- CI = Amount &#8211; Principle<\/p>\n\n\n\n<p><strong>Compound Amount &#8211; <\/strong>It is the total amount due at the end of the last period.<\/p>\n\n\n\n<p><strong>Frequency of Compounding &#8211; <\/strong>It indicates the number of times the interest is compounded in one year.<\/p>\n\n\n\n<p><strong>Compounding Period &#8211; <\/strong>The time period between two consecutive points in time at which interest is compounded.<\/p>\n\n\n\n<p>Let-<\/p>\n\n\n\n<p>P- Principal &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<\/p>\n\n\n\n<p>A&nbsp; &#8211; Amount<\/p>\n\n\n\n<p>i = interest on re. 1 for a year<\/p>\n\n\n\n<p>n = interest period<\/p>\n\n\n\n<p>The amount can be <a href=\"https:\/\/americannordicwalking.com\/press\/\" style=\"color: black\">americannordicwalking<\/a> calculated as below<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/ERQmpi5zPjM8Wat5DETF1wv5cpAFdQdJOa7Vhiqk8TSmzQYX7bgp1y6dus-qAk_4i9uTAFHoF6hMLapKvvv5AtJfrFjSGOMN-ZdPyaOi4DkJMfnlQZjElFrv6qJTrRWi6MWNBeuk\" alt=\"\"\/><\/figure>\n\n\n\n<p>And<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/flbIbymN2iINlgLwzgcuoPl2VQbco456K9li61W8gNG5YSnsHBnJggna0RtvPTZV8O7IqDlDIsS-FVacc7p-EpPiKYdMVJ2ZxenhEWOpQ5KOKlG3GfeqPQmPocYVPsyIyjmtBvwa\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Note-<\/strong> By using algorithm the above formula can be written as below-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/U6xlMxWiLM74mm3Gi2Kq_b4tl3Gg3b4bp_AkTAZtsphgYqGwoO0qdApu17y6PyZSdEZBVzHW-Jkas5a9md8nQCaBWjUC3FBLNiO-mGTX2LEk1S92BTzAA8W-eQiXeC7UR-EyeJYN\" alt=\"\"\/><\/figure>\n\n\n\n<p><strong>Note- <\/strong>if the compound interest is paid half-yearly, quarterly, monthly instead of a year there will be different formulae as given in the table below-<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Time<\/td><td>Amount<\/td><\/tr><tr><td>Annually<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/YJ8B8W7PrtFqPnv3YiAMs8CfN_UCMvSpH7igHbZ0vAnyVR6H3z8dAxWQMtBPnPANs5oGpWByTa7gcHdtZZjBfeW0iY-gbaX00bLnik3heV8W4aNJxE2n6YfmZWzRBxzrDCxPBpNo\" width=\"98\" height=\"23\"><\/td><\/tr><tr><td>Half-yearly<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/o186448GarNFO5QnTszAZobet6i7r3YCu_am1EPJ5CwuMy8rqyzmUx_-10hdO0oPTtoSjQ74wtAssaIx_XOO-PuqvF4e-OqtcRv7lVVyFUWT2ZPaLMy5BKMkafgbRg1k_e_D8XnG\" width=\"116\" height=\"43\"><\/td><\/tr><tr><td>Quarterly<\/td><td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/FPJ8_5FPhTBixrsHTh2Y1ibq-6gfTf2CrOdBxw4uYKljOxCNs3HiIh1W74ubu7XeHB-j1dJQGCM3fXX09znu_BcFzABnlu56PpxQkhmh8xFAo6ZZG7cwLL0-gtE0k2xY0BH6j_To\" width=\"119\" height=\"45\"><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Example:<\/strong> <strong>Aman invests 1000 rupees at 5 percent p.a for four years then find the compound interest on it.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>Here P = 1000, i = 0.05 and n = 4<\/p>\n\n\n\n<p>As we know that-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/kypJlUFpOUopSydB79kOF73DVBWXOhR5f5jDP6kzEE90bUHwkYIHWKVrvbLBvGAn7ts7dXpVe16RrdCA8c4A1eb94TRsKW-47UhLN9i0qtM88Q3TaQubgaltNPCRAmCphTRJG5yn\" alt=\"\"\/><\/figure>\n\n\n\n<p>So that on taking log, we get-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/GJ9HdeinF1PdtnV5lHju31xt2IQZwQNENzMMuhgyKkRGNd_YY4LQdaQV2mGmPGmzNiSOpsekPYVPquwHpldYHyBRGFjmzLvFCCLECEN9IVpk2VsReDqt2cEVYDP0xDxbDpqzfTgl\" alt=\"\"\/><\/figure>\n\n\n\n<p>So that the compound interest will be-<\/p>\n\n\n\n<p>C.I = 1215 &#8211; 1000 = 215<\/p>\n\n\n\n<p>This is the required answer.<\/p>\n\n\n\n<p><strong>Example: A sum of money invested at C.I. payable yearly amounts to 10, 816 Rs. at the end of the second year and to 11,248.64 Rs. at the end of the third year. Find the rate of interest and the sum.<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>Here A1 = 10,816, n = 2, and A2 = 11,248.64, n = 3<\/p>\n\n\n\n<p>We know that<\/p>\n\n\n\n<p>A = P (1 + i)n hence we get,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/U4nQKGKj41x-wqZANcnU1D1EjBceGGQCruZYZBGCGnWnsJip28nFYAJV7N0iNzI-0UfxeMDUTRrB3UaW1ospFlxwzZRRMUV6d85u9ofuMz3ollw14PygiuOUWs9QvW2SnG-pXoIh\" alt=\"\"\/><\/figure>\n\n\n\n<p>Here on dividing equation (2) by (1)-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/rFfUxBwj4MiuXkO8sH7UdZcEmZ7B-PzDzXLw5ULmsPsvDQ70gKl4EQJSEcjd5HDGvNp8LE7S5lfZk__3Mdy0rB61_dsVByr_x8iD0W4MAYecizCdpqVQlRvwNC0s5jeznYP-VHCB\" alt=\"\"\/><\/figure>\n\n\n\n<p>Therefore we get<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/6nJRHOS4IryPq8rHqTQG-aCl25KeA2U_T8tVp9pFJocN7Aq2_7b3WJBx5Abp6BpMtLtz0X88AKNL7TF_n_FbLs9hD0fSMESPwDioGDMzuyhlVDkDLDeJENJu6uf8qIMzV3GixTmV\" alt=\"\"\/><\/figure>\n\n\n\n<p>And<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/fiTv_ijg_2Go6awop6pkiXlP0htBKx9Itv2D0tBMvnz4V7eQ7d3ukUEaL0t5t8sSFgFwT3nowtHh0o4QhIuSIJH5bWOZoDsFeFmEps6jY5QUsH_IWUCQUeXfNE9kx6ASOH70m3Zk\" alt=\"\"\/><\/figure>\n\n\n\n<p>Hence the rate is 4 percent.<\/p>\n\n\n\n<p>From first equation-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/hskLOx58p0UUdhrzZArSUMVOM5PKkWT1k-CpsV8Jubb9I0TDA5c4wVvrgTAMUic-nG5ASCzM6TdgtdwRHvTC25gyJh8lhU54iWN9XoYCSbhPWMhUI5njnPLW9r9NorIixbWlag6s\" alt=\"\"\/><\/figure>\n\n\n\n<p>Or<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/XjP6mMaIzYSJNbHcrIHITScSZACoa5ZIMAVj7DH9wtzd-BOupopQyUUAYLqw0groye30Q339uEYfSSTvoSjt_39pDJqmYCaW-RXbazAn9ieu604B_SD6PvvqQm9hciWpThMklnnx\" alt=\"\"\/><\/figure>\n\n\n\n<p>Now<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/NQlUstJv01hkplT_m9ad4cWSEOSQ1ORVj9h7pQSW3-wWumGuRvPx84hMq-cdzrkGNUHQdO_JwZde-lM30nDhwgzyCd5zDLbvkRArCP1vAUA4kF16mrWuhTX0qOrRikjAyw9qPDc-\" alt=\"\"\/><\/figure>\n\n\n\n<p>P = antilog 4.000 = 10,000<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Nominal and effective rate of interest<\/strong><\/h2>\n\n\n\n<p>Nominal rate of interest is the rate of interest per annum which is compounded yearly, half yearly, quarterly, monthly, n times in a year or continuously.<\/p>\n\n\n\n<p>Effective rate of interest is the rate of interest per annum compounded only once in a year.<\/p>\n\n\n\n<p>There is a relationships between nominal and effective rate of interest under two different conditions-<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; If compounding is \u2018n\u2019 times in a year-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Uk4GK8Ilj1sY3he9reP09lqUVP-EtswTYQb8CC6Hp_FSKXDTlaYMpVXexKsC-WQ3ROmC4WzV0scvHtmPUBFYNd4-Nf3EjDMjOzlKoXIpaGcpWWUKcGzkHGPNAjydyvqrl9HrSpcF\" alt=\"\"\/><\/figure>\n\n\n\n<p>Where \u2018r\u2019 is nominal rate and \u2018R\u2019 is effective rate.<\/p>\n\n\n\n<p>1. &nbsp; &nbsp; If compounding is continuous-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/GsEzzEq0IlW9vvgzGoRCgnk2RhAbL7erEH3t7xq4NUWyEGoyeSIT1UCMX9ABPjbjRptghWq-wRom00wRhRmf1PE87PakvLFLhLDEgW9LYyc4EBdeeavkQNkiDxGIOM4r8W065C1k\" alt=\"\"\/><\/figure>\n\n\n\n<p>Or<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/0X64TETTHbHYmBra9yMsUkB8xf5v9PE_MPWyLdIFrD1Bp_cpFvr4LWMlQJMDo0AaSsXitoSWFOjTDd8o8W7i6eWm5e5iOHgywig4cmACLVXr5fH_UdhWinL6bTgERkquQHxvEi4o\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Relationship between two nominal rates<\/strong><\/h2>\n\n\n\n<p>If interest is compounded quarterly at r1 percent and the interest is compounded half yearly at&nbsp; r2 percent,<\/p>\n\n\n\n<p>the relationship between the two is-<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/JS0Ln9Qv904eb2T00-UtGp0a6jXjSlpklDZAkpZOFnsy1PSXZOFQRnvui6uwQqVEmApOMEhH0piDlzW8VEj59X3YkHnOxR1pm5D7E8fsYMF_YH0xKrM_qODiWXwNlAoqe363jYc7\" alt=\"\"\/><\/figure><\/div>\n\n\n<p><strong>Example: Ronak deposited Rs. 10,000 in a bank for 3 years<\/strong> and <strong>Bank gives two offers either 10 percent compounded quarterly or 8% compounded continuously, then which offer is preferable for Ronak?<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong><\/p>\n\n\n\n<p>Balance after three years under first offer-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/-XgLal5OhFLBMezpzJmR5PgrnI6vaGrTHLkVl4KnvgvB34sC3McWtzTiV3sQ1UpApyhLCalKdqu7vBQ9AaPw_zAoB_lHVwn6yXjBIuL1ybwYvFmBRL4AxLYCVWRPODdif9zUdQDo\" alt=\"\"\/><\/figure>\n\n\n\n<p>Balance after 3 years under second offer-<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/2U9BAIwRlgCYU3U2064EKmrXx0VQecMyObPH5kqOX21D8_5WV56FRAQZ7sRBzxG-94121N5aChwIJZzN9CgjCsk9Ngh52W0ML9edkRr8zxqe3swC-KA1HpUtMXtuOILtHnBLCmeo\" alt=\"\"\/><\/figure>\n\n\n\n<p>Hence the first offer is preferable.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>compound interest is calculated on interest as well as on principal. Therefore, compound interest is sometimes described as \u2018interest on interest\u2019.<\/p>\n","protected":false},"author":28,"featured_media":4997,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[31],"tags":[],"class_list":["post-7340","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.3.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is compound interest? - Goseeko blog<\/title>\n<meta name=\"description\" content=\"compound interest is calculated on interest as well as on principal. 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