{"id":179733,"date":"2025-01-02T06:13:10","date_gmt":"2025-01-02T06:13:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=179733"},"modified":"2025-01-02T06:13:14","modified_gmt":"2025-01-02T06:13:14","slug":"sally-has-two-iras","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/02\/sally-has-two-iras\/","title":{"rendered":"Sally has two IRA\u2019s"},"content":{"rendered":"\n<p>Sally has two IRA\u2019s. IRA #1 earns interest at 5% effectiveannually andIRA #2 earns interest at 12% effective annually. She has notmade anycontributions since January 1, 1999, when the amount in IRA #1was twicethe amount in IRA #2. The sum of the two accounts on January1, 1993was $95,000. Determine how much was in IRA #2 on January 1,1985.<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To determine the balance in IRA #2 on January 1, 1985, we need to work backward from the information provided:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>IRA #1<\/strong> earns 5% interest compounded annually.<\/li>\n\n\n\n<li><strong>IRA #2<\/strong> earns 12% interest compounded annually.<\/li>\n\n\n\n<li>On January 1, 1999, the amount in IRA #1 was twice that in IRA #2.<\/li>\n\n\n\n<li>The combined balance of both accounts on January 1, 1993, was $95,000.<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 1: Define Variables<\/strong><\/p>\n\n\n\n<p>Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( x ) be the balance in IRA #2 on January 1, 1985.<\/li>\n\n\n\n<li>( 2x ) be the balance in IRA #1 on January 1, 1985.<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2: Calculate Account Balances on January 1, 1993<\/strong><\/p>\n\n\n\n<p>The time between January 1, 1985, and January 1, 1993, is 8 years. Using the compound interest formula:<\/p>\n\n\n\n<p>[ A = P \\times (1 + r)^t ]<\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( A ) is the amount after time ( t ),<\/li>\n\n\n\n<li>( P ) is the principal amount,<\/li>\n\n\n\n<li>( r ) is the annual interest rate,<\/li>\n\n\n\n<li>( t ) is the time in years.<\/li>\n<\/ul>\n\n\n\n<p>For IRA #1:<br>[ A_1 = 2x \\times (1 + 0.05)^8 = 2x \\times 1.477456 ]<\/p>\n\n\n\n<p>For IRA #2:<br>[ A_2 = x \\times (1 + 0.12)^8 = x \\times 2.518171 ]<\/p>\n\n\n\n<p>The total balance on January 1, 1993, is the sum of ( A_1 ) and ( A_2 ):<\/p>\n\n\n\n<p>[ A_1 + A_2 = 2x \\times 1.477456 + x \\times 2.518171 = 95,000 ]<\/p>\n\n\n\n<p>Simplifying:<\/p>\n\n\n\n<p>[ x \\times (2.954912 + 2.518171) = 95,000 ]<\/p>\n\n\n\n<p>[ x \\times 5.473083 = 95,000 ]<\/p>\n\n\n\n<p>Solving for ( x ):<\/p>\n\n\n\n<p>[ x = \\frac{95,000}{5.473083} ]<\/p>\n\n\n\n<p>[ x \\approx 17,353.47 ]<\/p>\n\n\n\n<p><strong>Step 3: Calculate IRA #2 Balance on January 1, 1985<\/strong><\/p>\n\n\n\n<p>The balance in IRA #2 on January 1, 1985, was approximately $17,353.47.<\/p>\n\n\n\n<p><strong>Step 4: Verify the Calculation<\/strong><\/p>\n\n\n\n<p>To ensure accuracy, let&#8217;s calculate the balances on January 1, 1993:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>IRA #1: ( 2 \\times 17,353.47 \\times 1.477456 \\approx 51,707.94 )<\/li>\n\n\n\n<li>IRA #2: ( 17,353.47 \\times 2.518171 \\approx 43,292.06 )<\/li>\n<\/ul>\n\n\n\n<p>Total: ( 51,707.94 + 43,292.06 = 95,000 ), which matches the given total.<\/p>\n\n\n\n<p>Therefore, the balance in IRA #2 on January 1, 1985, was approximately $17,353.47.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sally has two IRA\u2019s. IRA #1 earns interest at 5% effectiveannually andIRA #2 earns interest at 12% effective annually. She has notmade anycontributions since January 1, 1999, when the amount in IRA #1was twicethe amount in IRA #2. The sum of the two accounts on January1, 1993was $95,000. Determine how much was in IRA #2 [&hellip;]<\/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-179733","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179733","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=179733"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/179733\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=179733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=179733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=179733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}