{"id":218710,"date":"2025-05-24T10:39:20","date_gmt":"2025-05-24T10:39:20","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=218710"},"modified":"2025-05-24T10:39:22","modified_gmt":"2025-05-24T10:39:22","slug":"solve-each-of-the-following-equations-for-the-indicated-variable","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/24\/solve-each-of-the-following-equations-for-the-indicated-variable\/","title":{"rendered":"Solve each of the following equations for the indicated variable."},"content":{"rendered":"\n
Solve each of the following equations for the indicated variable.<\/p>\n\n\n\n
(a) I = Prt for r (b) S = P(1 + rt) for t (c) D = rL for r (d) FV = PMT p for PMT (a) r = Pt\/S<\/p>\n\n\n\n
(b) t = (S – P)\/(Pr)<\/p>\n\n\n\n
(c) r = D\/L<\/p>\n\n\n\n
(d) PMT = FV\/p<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n\n\n\n\n
Solved Equations:<\/strong><\/h3>\n\n\n\n
(a)<\/strong> I=PrtI = Prt for rr r=IPtr = \\frac{I}{Pt}<\/p>\n\n\n\n\n\n\n\n
Solving equations for a particular variable involves using algebraic rules to isolate that variable on one side of the equation. This process is foundational in mathematics and essential for applying formulas in various fields like finance, physics, and engineering.<\/p>\n\n\n\n
(a) I=PrtI = Prt for rr:<\/strong> This equation represents the simple interest formula, where II is the interest earned, PP is the principal amount, rr is the rate, and tt is the time. To isolate rr, divide both sides of the equation by PtPt, yielding r=IPtr = \\frac{I}{Pt}.<\/p>\n\n\n\n
(b) S=P(1+rt)S = P(1 + rt) for tt:<\/strong> This is the formula for the future value SS with simple interest. Start by dividing both sides by PP to get SP=1+rt\\frac{S}{P} = 1 + rt. Subtract 1 from both sides to get S\u2212PP=rt\\frac{S – P}{P} = rt. Finally, divide both sides by rr to isolate tt: t=S\u2212PPrt = \\frac{S – P}{Pr}<\/p>\n\n\n\n
(c) D=rLD = rL for rr:<\/strong> This is a basic linear equation. Divide both sides by LL to isolate rr: r=DLr = \\frac{D}{L}<\/p>\n\n\n\n
(d) FV=PMT\u22c5pFV = PMT \\cdot p for PMTPMT:<\/strong> Here, FVFV is the future value of periodic payments, PMTPMT is the payment per period, and pp is the number of periods. Divide both sides by pp to solve for PMTPMT: PMT=FVpPMT = \\frac{FV}{p}<\/p>\n\n\n\n
These transformations help interpret and apply formulas flexibly based on known and unknown quantities.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
Solve each of the following equations for the indicated variable. (a) I = Prt for r(b) S = P(1 + rt) for t(c) D = rL for r(d) FV = PMT p for PMT(a) r = Pt\/S (b) t = (S – P)\/(Pr) (c) r = D\/L (d) PMT = FV\/p The Correct Answer and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-218710","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218710","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=218710"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/218710\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=218710"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=218710"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=218710"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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<\/figure>\n","protected":false},"excerpt":{"rendered":"