{"id":23254,"date":"2025-06-17T11:27:08","date_gmt":"2025-06-17T11:27:08","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=23254"},"modified":"2025-06-17T11:27:11","modified_gmt":"2025-06-17T11:27:11","slug":"trevor-has-an-investment-worth-6774-50","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/trevor-has-an-investment-worth-6774-50\/","title":{"rendered":"Trevor has an investment worth $6,774.50"},"content":{"rendered":"\n<p>Trevor has an investment worth $6,774.50. He made his only deposit in it 22 years ago. Given that the investment yields 2.7% simple interest annually, how big was the initial deposit?<\/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 initial deposit (principal) Trevor made 22 years ago, given the current value and interest rate under <strong>simple interest<\/strong>, we use the <strong>simple interest formula<\/strong>: A=P(1+rt)A = P(1 + rt)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>AA is the final amount (total value of the investment) = <strong>$6,774.50<\/strong><\/li>\n\n\n\n<li>PP is the principal (initial deposit) = <strong>?<\/strong><\/li>\n\n\n\n<li>rr is the annual interest rate = <strong>2.7% = 0.027<\/strong><\/li>\n\n\n\n<li>tt is the time in years = <strong>22<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Plug into the formula<\/h3>\n\n\n\n<p>6,774.50=P(1+0.027\u00d722)6,774.50 = P(1 + 0.027 \\times 22)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the interest term<\/h3>\n\n\n\n<p>0.027\u00d722=0.5940.027 \\times 22 = 0.594 1+0.594=1.5941 + 0.594 = 1.594<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve for PP<\/h3>\n\n\n\n<p>6,774.50=P\u00d71.5946,774.50 = P \\times 1.594 P=6,774.501.594P = \\frac{6,774.50}{1.594} P\u22484,248.68P \\approx 4,248.68<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p><strong>Trevor\u2019s initial deposit was approximately $4,248.68.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd8 Explanation (300 words):<\/h3>\n\n\n\n<p>Simple interest is a method of calculating interest where the interest amount is based only on the <strong>original principal<\/strong> over a period of time. The formula A=P(1+rt)A = P(1 + rt) combines the principal, the interest rate per year, and the time in years to determine the total accumulated amount.<\/p>\n\n\n\n<p>In Trevor&#8217;s case, the current investment is worth $6,774.50 after 22 years, and the interest rate is 2.7% per year. Since he made only one deposit, the only way this amount could grow is through accumulating interest on the original amount each year, without compounding.<\/p>\n\n\n\n<p>Using the formula, we calculated the total growth multiplier as 1+(0.027\u00d722)=1.5941 + (0.027 \\times 22) = 1.594. This means his investment grew by about 59.4% over the 22 years. To find the original investment, we reversed the process by dividing the final amount by the multiplier: 6,774.50\u00f71.594\u22484,248.686,774.50 \\div 1.594 \\approx 4,248.68.<\/p>\n\n\n\n<p>This tells us that Trevor initially deposited about <strong>$4,248.68<\/strong>, and over 22 years, it earned about <strong>$2,525.82<\/strong> in interest (6,774.50 \u2013 4,248.68), thanks to the consistent simple interest rate of 2.7%.<\/p>\n\n\n\n<p>This calculation is crucial in financial planning and shows how interest rates and time affect investment growth, especially under different interest models like simple or compound interest.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Trevor has an investment worth $6,774.50. He made his only deposit in it 22 years ago. Given that the investment yields 2.7% simple interest annually, how big was the initial deposit? The correct answer and explanation is: To find the initial deposit (principal) Trevor made 22 years ago, given the current value and interest rate [&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-23254","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23254","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=23254"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23254\/revisions"}],"predecessor-version":[{"id":23255,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/23254\/revisions\/23255"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=23254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=23254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=23254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}