{"id":35613,"date":"2025-06-24T13:05:53","date_gmt":"2025-06-24T13:05:53","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=35613"},"modified":"2025-06-24T13:05:57","modified_gmt":"2025-06-24T13:05:57","slug":"calculate-to-the-nearest-cent-the-future-value-fv-in-dollars-of-an-investment-of-10000-at-the-stated-interest-rate-after-the-stated-amount-of-time","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/calculate-to-the-nearest-cent-the-future-value-fv-in-dollars-of-an-investment-of-10000-at-the-stated-interest-rate-after-the-stated-amount-of-time\/","title":{"rendered":"Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time"},"content":{"rendered":"\n<p>Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time. 0.3% per month, compounded monthly, after 21 years<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>The future value (FV) is <strong>$18,495.74<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation:<\/strong><\/p>\n\n\n\n<p>To calculate the future value of an investment with compound interest, we use the <strong>compound interest formula<\/strong>: FV=P(1+r)nFV = P(1 + r)^n<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>PP = Initial principal = $10,000<\/li>\n\n\n\n<li>rr = Monthly interest rate = 0.3% = 0.003<\/li>\n\n\n\n<li>nn = Total number of compounding periods = 21 years \u00d7 12 months\/year = 252 months<\/li>\n<\/ul>\n\n\n\n<p>Substitute the values into the formula: FV=10,000(1+0.003)252FV = 10,000(1 + 0.003)^{252} FV=10,000(1.003)252FV = 10,000(1.003)^{252}<\/p>\n\n\n\n<p>Now calculate: 1.003252\u22481.8495741.003^{252} \u2248 1.849574 FV\u224810,000\u00d71.849574=18,495.74FV \u2248 10,000 \u00d7 1.849574 = 18,495.74<\/p>\n\n\n\n<p>So, the investment grows to <strong>$18,495.74<\/strong> after 21 years with monthly compounding at 0.3% per month.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>This result shows how small monthly interest rates can significantly grow an investment over a long period due to compound interest. Each month, the earned interest is added to the principal, and the next month&#8217;s interest is calculated on this increased amount. Even though 0.3% seems small, when compounded over 252 months, the money nearly doubles. Long-term investments with regular compounding benefit greatly even at modest rates, making compound interest a powerful tool for wealth accumulation.<\/p>\n\n\n\n<p><a href=\"https:\/\/www.numerade.com\/ask\/question\/calculate-to-the-nearest-cent-the-future-value-fv-in-dollars-of-an-investment-of-10000-at-the-stated-interest-rate-after-the-stated-amount-of-time-03-per-month-compounded-monthly-after-21-ye-58912\/\" target=\"_blank\" rel=\"noopener\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate, to the nearest cent, the future value FV (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time. 0.3% per month, compounded monthly, after 21 years The correct answer and explanation is: Correct Answer:The future value (FV) is $18,495.74. Explanation: To calculate the future value of [&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-35613","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35613","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=35613"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35613\/revisions"}],"predecessor-version":[{"id":35614,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/35613\/revisions\/35614"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=35613"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=35613"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=35613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}