{"id":214577,"date":"2025-05-15T04:33:44","date_gmt":"2025-05-15T04:33:44","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=214577"},"modified":"2025-05-15T04:33:46","modified_gmt":"2025-05-15T04:33:46","slug":"for-each-given-interest-rate-determine-which-option-is-better","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/15\/for-each-given-interest-rate-determine-which-option-is-better\/","title":{"rendered":"For each given interest rate, determine which option is better"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">For each given interest rate, determine which option is better. Your first option is to receive $70,000 today, which will be put in a bank and left to compound for the next 40 years.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To determine whether receiving <strong>\\$70,000 today<\/strong> is better than an unspecified second option (perhaps receiving a future amount), we need to analyze how much that \\$70,000 would grow if invested at different interest rates over <strong>40 years<\/strong> using <strong>compound interest<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We\u2019ll use the <strong>compound interest formula<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>A = P(1 + r)^t<br>$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$A$ = Future value of the investment<\/li>\n\n\n\n<li>$P$ = Principal amount (\\$70,000)<\/li>\n\n\n\n<li>$r$ = Annual interest rate (as a decimal)<\/li>\n\n\n\n<li>$t$ = Time (40 years)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let\u2019s compute the future value of \\$70,000 under different interest rates:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 At <strong>4% Interest<\/strong>:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>A = 70,000(1 + 0.04)^{40} = 70,000(4.801) \u2248 336,070<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 At <strong>6% Interest<\/strong>:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>A = 70,000(1 + 0.06)^{40} = 70,000(10.286) \u2248 720,020<br>$$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd39 At <strong>8% Interest<\/strong>:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">$$<br>A = 70,000(1 + 0.08)^{40} = 70,000(21.724) \u2248 1,520,680<br>$$<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">Now, to decide <strong>which option is better<\/strong>, we compare these results to the future value of the alternative option (which we assume is a fixed future amount). Suppose your second option is to receive <strong>\\$500,000 in 40 years<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Compare:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>At <strong>4%<\/strong>, \\$70,000 today grows to <strong>\\$336,070<\/strong> \u2192 <strong>\\$500,000 in 40 years is better<\/strong><\/li>\n\n\n\n<li>At <strong>6%<\/strong>, \\$70,000 today grows to <strong>\\$720,020<\/strong> \u2192 <strong>\\$70,000 today is better<\/strong><\/li>\n\n\n\n<li>At <strong>8%<\/strong>, \\$70,000 today grows to <strong>\\$1,520,680<\/strong> \u2192 <strong>\\$70,000 today is much better<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Conclusion:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>If the interest rate is below ~5.6%<\/strong>, it\u2019s better to wait and receive the future amount (e.g., \\$500,000).<\/li>\n\n\n\n<li><strong>If the interest rate is above ~5.6%<\/strong>, taking the \\$70,000 today and investing it is better.<\/li>\n\n\n\n<li>The higher the interest rate, the more valuable money is <strong>today<\/strong> due to compounding.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the better option depends entirely on the <strong>interest rate<\/strong> and the <strong>future value of the second option<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>For each given interest rate, determine which option is better. Your first option is to receive $70,000 today, which will be put in a bank and left to compound for the next 40 years. The Correct Answer and Explanation is: To determine whether receiving \\$70,000 today is better than an unspecified second option (perhaps receiving [&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-214577","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214577","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=214577"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/214577\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=214577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=214577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=214577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}