{"id":16568,"date":"2025-06-11T16:16:45","date_gmt":"2025-06-11T16:16:45","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16568"},"modified":"2025-06-11T16:17:02","modified_gmt":"2025-06-11T16:17:02","slug":"find-the-future-value-of-a-6300-investment-if-the-interest-rate-is-5-75-compounded-monthly-for-4-years","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-future-value-of-a-6300-investment-if-the-interest-rate-is-5-75-compounded-monthly-for-4-years\/","title":{"rendered":"Find the future value of a $6300 investment if the interest rate is 5.75% compounded monthly for 4 years"},"content":{"rendered":"\n<p>Find the future value of a $6300 investment if the interest rate is 5.75% compounded monthly for 4 years. (Round your answer to two decimal places.)<\/p>\n\n\n\n<p><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>To find the <strong>future value<\/strong> of a $6300 investment at a <strong>5.75% annual interest rate compounded monthly<\/strong> for <strong>4 years<\/strong>, we use the <strong>compound interest formula<\/strong>: A=P(1+rn)ntA = P \\left(1 + \\frac{r}{n}\\right)^{nt}<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA is the future value (what we are solving for)<\/li>\n\n\n\n<li>PP is the principal amount = $6300<\/li>\n\n\n\n<li>rr is the annual interest rate = 0.0575<\/li>\n\n\n\n<li>nn is the number of compounding periods per year = 12 (monthly)<\/li>\n\n\n\n<li>tt is the number of years = 4<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step-by-step Calculation:<\/h3>\n\n\n\n<p>A=6300(1+0.057512)12\u00d74A = 6300 \\left(1 + \\frac{0.0575}{12} \\right)^{12 \\times 4} A=6300(1+0.0047916667)48A = 6300 \\left(1 + 0.0047916667 \\right)^{48} A=6300(1.0047916667)48A = 6300 \\left(1.0047916667\\right)^{48} A=6300\u00d71.270244388A = 6300 \\times 1.270244388 A\u22487992.54A \\approx 7992.54<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p><strong>$7992.54<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">300-Word Explanation:<\/h3>\n\n\n\n<p>Compound interest is a powerful financial concept where interest is calculated on both the initial principal and on the accumulated interest of previous periods. This makes it different\u2014and often more beneficial\u2014than simple interest, where only the principal earns interest.<\/p>\n\n\n\n<p>In this case, we are dealing with <strong>monthly compounding<\/strong>, which means the interest is added to the investment every month. The more frequently interest is compounded, the greater the total return, because interest is calculated more often on an increasing balance.<\/p>\n\n\n\n<p>The investment starts at $6300, with a <strong>5.75% annual interest rate<\/strong>. However, because the compounding occurs <strong>monthly<\/strong>, the annual rate is divided by 12, giving a monthly rate of approximately 0.00479 (or 0.479%). The investment period is <strong>4 years<\/strong>, so there are 4\u00d712=484 \\times 12 = 48 compounding periods.<\/p>\n\n\n\n<p>By plugging the values into the <strong>compound interest formula<\/strong>, we calculate that after 4 years, the investment will grow to <strong>$7992.54<\/strong>. This means the investment earned about <strong>$1692.54<\/strong> in interest over the 4 years.<\/p>\n\n\n\n<p>Understanding compound interest is essential for both short- and long-term financial planning. Whether investing, saving, or borrowing, the frequency of compounding can significantly affect your total gains or costs. In this example, monthly compounding maximizes growth by frequently adding interest, making your money work harder for you.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the future value of a $6300 investment if the interest rate is 5.75% compounded monthly for 4 years. (Round your answer to two decimal places.) The correct answer and explanation is: To find the future value of a $6300 investment at a 5.75% annual interest rate compounded monthly for 4 years, we use the [&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-16568","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16568","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=16568"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16568\/revisions"}],"predecessor-version":[{"id":16571,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16568\/revisions\/16571"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16568"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16568"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16568"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}