{"id":90685,"date":"2025-06-01T10:33:39","date_gmt":"2025-06-01T10:33:39","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90685"},"modified":"2025-06-01T10:33:39","modified_gmt":"2025-06-01T10:33:39","slug":"suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/","title":{"rendered":"Suppose a bank gives an interest of 10% per annum compounded annually"},"content":{"rendered":"

Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same?<\/p>\n

[amp_mcq option1=”10%” option2=”10.5%” option3=”11%” option4=”12%” correct=”option2″]<\/p>\n

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This question was previously asked in<\/div>\n
UPSC CAPF – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + \\frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + \\text{Interest} = P + \\frac{P \\times R_{SI} \\times 2}{100} = P(1 + \\frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + \\frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + \\frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = \\frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = \\frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum.<\/section>\n
The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.<\/section>\n
Over a period of more than one year, compound interest will always yield a higher maturity amount than simple interest for the same principal and nominal rate, because interest earned in previous periods also earns interest. To get the same maturity amount, the simple interest rate must be higher than the compound interest rate (except for the first year, where they are equal).<\/section>\n","protected":false},"excerpt":{"rendered":"

Suppose a bank gives an interest of 10% per annum compounded annually for a fixed deposit for a period of two years. What should be the simple interest rate per annum if the maturity amount after two years is to remain the same? [amp_mcq option1=”10%” option2=”10.5%” option3=”11%” option4=”12%” correct=”option2″] This question was previously asked in … <\/p>\n

Detailed SolutionSuppose a bank gives an interest of 10% per annum compounded annually<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1085],"tags":[1108,1102],"class_list":["post-90685","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nSuppose a bank gives an interest of 10% per annum compounded annually<\/title>\n<meta name=\"description\" content=\"Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + text{Interest} = P + frac{P times R_{SI} times 2}{100} = P(1 + frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum. The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Suppose a bank gives an interest of 10% per annum compounded annually\" \/>\n<meta property=\"og:description\" content=\"Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + text{Interest} = P + frac{P times R_{SI} times 2}{100} = P(1 + frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum. The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:33:39+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Suppose a bank gives an interest of 10% per annum compounded annually","description":"Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + text{Interest} = P + frac{P times R_{SI} times 2}{100} = P(1 + frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum. The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/","og_locale":"en_US","og_type":"article","og_title":"Suppose a bank gives an interest of 10% per annum compounded annually","og_description":"Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + text{Interest} = P + frac{P times R_{SI} times 2}{100} = P(1 + frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum. The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:33:39+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/","url":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/","name":"Suppose a bank gives an interest of 10% per annum compounded annually","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:33:39+00:00","dateModified":"2025-06-01T10:33:39+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"Let the principal amount be P. For compound interest at 10% per annum compounded annually for 2 years, the maturity amount is $A_{CI} = P(1 + \\frac{10}{100})^2 = P(1.1)^2 = 1.21P$. For simple interest over 2 years with an annual rate $R_{SI}$, the maturity amount is $A_{SI} = P + \\text{Interest} = P + \\frac{P \\times R_{SI} \\times 2}{100} = P(1 + \\frac{2R_{SI}}{100})$. For the maturity amounts to be the same, $1.21P = P(1 + \\frac{2R_{SI}}{100})$. Dividing by P (assuming P > 0), we get $1.21 = 1 + \\frac{2R_{SI}}{100}$. Subtracting 1 from both sides, $0.21 = \\frac{2R_{SI}}{100}$. Multiplying by 100, $21 = 2R_{SI}$. Therefore, $R_{SI} = \\frac{21}{2} = 10.5$. The simple interest rate should be 10.5% per annum. The problem requires comparing the maturity amounts obtained from compound interest and simple interest over the same period and finding the equivalent simple interest rate that yields the same amount.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/suppose-a-bank-gives-an-interest-of-10-per-annum-compounded-annually\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Suppose a bank gives an interest of 10% per annum compounded annually"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90685","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=90685"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90685\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90685"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90685"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90685"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}