{"id":22955,"date":"2025-06-17T08:34:05","date_gmt":"2025-06-17T08:34:05","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=22955"},"modified":"2025-06-17T08:34:07","modified_gmt":"2025-06-17T08:34:07","slug":"a-total-of-32000-is-invested-in-two-bonds-that-pay-6-25-and-5-75-simple-interest","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-total-of-32000-is-invested-in-two-bonds-that-pay-6-25-and-5-75-simple-interest\/","title":{"rendered":"A total of 32,000 is invested in two bonds that pay 6.25% and 5.75% simple interest"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">A total of 32,000 is invested in two bonds that pay 6.25% and 5.75% simple interest. The investor wants an annual interest income of 19000 from the investments. What amount should be invested in the 6.25% bond?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve this problem, we can use a system of equations involving simple interest. Let\u2019s define the variables first:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>xx = amount invested in the 6.25% bond<\/li>\n\n\n\n<li>32000\u2212x32000 &#8211; x = amount invested in the 5.75% bond<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The formula for <strong>simple interest<\/strong> is: Interest=Principal\u00d7Rate\\text{Interest} = \\text{Principal} \\times \\text{Rate}<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Set up the interest equations<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The total interest from both investments should equal $19,000. So: 0.0625x+0.0575(32000\u2212x)=190000.0625x + 0.0575(32000 &#8211; x) = 19000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Solve the equation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Distribute the 0.0575: 0.0625x+(0.0575\u00d732000)\u22120.0575x=190000.0625x + (0.0575 \\times 32000) &#8211; 0.0575x = 19000 0.0625x+1840\u22120.0575x=190000.0625x + 1840 &#8211; 0.0575x = 19000 (0.0625\u22120.0575)x+1840=19000(0.0625 &#8211; 0.0575)x + 1840 = 19000 0.005x+1840=190000.005x + 1840 = 19000<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Subtract 1840 from both sides: 0.005x=171600.005x = 17160<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Divide both sides by 0.005: x=171600.005=3,432,000x = \\frac{17160}{0.005} = 3,432,000<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>$3,432,000<\/strong> should be invested in the <strong>6.25% bond<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words):<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This problem is based on <strong>simple interest<\/strong>, which is calculated by multiplying the principal (amount of money invested), the annual interest rate (as a decimal), and time in years. In this case, the time is 1 year, so we only consider the product of the principal and rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We\u2019re given that a total of $32,000 is split between two bonds\u2014one paying 6.25% and the other 5.75%. The investor desires a total annual income of $19,000. We define the unknown amount invested in the higher-interest bond (6.25%) as xx, and the remaining amount (in the 5.75% bond) as 32000\u2212x32000 &#8211; x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The key is to write expressions for the interest generated by each bond using the simple interest formula and then add them to match the desired total interest. After forming the equation, solving it requires basic algebra\u2014distribute, combine like terms, isolate the variable, and then solve.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Notably, the resulting required investment of $3,432,000 is <strong>far more than the original total of $32,000<\/strong>, which signals a problem: the investor is trying to earn <strong>$19,000<\/strong> from just <strong>$32,000<\/strong> in one year, which is <strong>an unrealistic goal<\/strong> at interest rates of around 6%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, <strong>there is no possible way<\/strong> to divide $32,000 between those bonds and earn $19,000 in interest per year. The equation gives a mathematically correct investment, but it doesn&#8217;t align with the reality of the available capital.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So:<br>\u2705 <strong>Correct math<\/strong><br>\u274c <strong>Not feasible with only $32,000 capital<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A total of 32,000 is invested in two bonds that pay 6.25% and 5.75% simple interest. The investor wants an annual interest income of 19000 from the investments. What amount should be invested in the 6.25% bond? The correct answer and explanation is: To solve this problem, we can use a system of equations involving [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-22955","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=22955"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22955\/revisions"}],"predecessor-version":[{"id":22956,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/22955\/revisions\/22956"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=22955"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=22955"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=22955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}