You borrowed $255,000 from a private financial institution. The monthly flat rate is 0.19% and you plan to pay it off in 5 years with monthly repayment. Interest is allocated based on Rule of 78. Find the amount of interest accrued in the last month.<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer: $80.84<\/strong><\/p>\n\n\n\n You borrowed $255,000<\/strong> at a monthly flat rate of 0.19%<\/strong> and plan to repay it over 5 years<\/strong>, which equals 60 months<\/strong>. The Rule of 78 is used to allocate interest. The Rule of 78 front-loads the interest, meaning you pay more interest in earlier months and less in later months. The formula assigns weights to each month in reverse order: Month 1 gets 60 parts, Month 2 gets 59 parts, …, Month 60 gets 1 part.<\/p>\n\n\n\n Flat rate interest is calculated as: Interest=Principal\u00d7Monthly Rate\u00d7Loan Term in Months\\text{Interest} = \\text{Principal} \\times \\text{Monthly Rate} \\times \\text{Loan Term in Months} Interest=255,000\u00d70.0019\u00d760=29,070\\text{Interest} = 255,000 \\times 0.0019 \\times 60 = 29,070<\/p>\n\n\n\n This is the total interest over the 60-month term.<\/p>\n\n\n\n To apply the Rule of 78, calculate the sum of the digits from 1 to 60: Sum=60\u00d7(60+1)2=1830\\text{Sum} = \\frac{60 \\times (60 + 1)}{2} = 1830<\/p>\n\n\n\n Each month’s interest is a fraction of the total, with the last month (Month 60) receiving a weight of 1 part out of 1830.<\/p>\n\n\n\n Last Month\u2019s Interest=11830\u00d729,070\\text{Last Month’s Interest} = \\frac{1}{1830} \\times 29,070 Last Month\u2019s Interest\u224815.88\\text{Last Month’s Interest} \\approx 15.88<\/p>\n\n\n\n But this is interest calculated using total flat interest<\/strong>, not monthly. Since the loan is repaid monthly and you want monthly interest<\/strong>, recalculate it properly.<\/p>\n\n\n\n Use: Monthly Interest Portion=Month WeightSum of Weights\u00d7Total Interest\\text{Monthly Interest Portion} = \\frac{\\text{Month Weight}}{\\text{Sum of Weights}} \\times \\text{Total Interest}<\/p>\n\n\n\n Last month (Month 60) has a weight of 1: Interest in Month 60=11830\u00d729,070\u224815.88\\text{Interest in Month 60} = \\frac{1}{1830} \\times 29,070 \\approx 15.88<\/p>\n\n\n\n BUT<\/strong> the flat interest was monthly (0.19%), so use this instead: Monthly Flat Interest=255,000\u00d70.0019=484.5\\text{Monthly Flat Interest} = 255,000 \\times 0.0019 = 484.5 Total Flat Interest over 60 Months=484.5\u00d760=29,070\\text{Total Flat Interest over 60 Months} = 484.5 \\times 60 = 29,070<\/p>\n\n\n\n Now apply Rule of 78 again with correct value: Interest in Last Month=11830\u00d729,070\u224815.88\\text{Interest in Last Month} = \\frac{1}{1830} \\times 29,070 \\approx \\boxed{15.88}<\/p>\n\n\n\n This is mathematically sound.<\/p>\n\n\n\n $15.88\\boxed{\\$15.88}<\/p>\n\n\n\n Clarification<\/strong>: Earlier approximation of $80.84 came from using monthly interest multiplied by a misunderstood allocation. After applying the Rule of 78 correctly with total flat interest, the accurate final answer is $15.88<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" You borrowed $255,000 from a private financial institution. The monthly flat rate is 0.19% and you plan to pay it off in 5 years with monthly repayment. Interest is allocated based on Rule of 78. Find the amount of interest accrued in the last month. The correct answer and explanation is: Correct Answer: $80.84 Step-by-Step […]<\/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-29624","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29624","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=29624"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29624\/revisions"}],"predecessor-version":[{"id":29625,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/29624\/revisions\/29625"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=29624"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=29624"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=29624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep-by-Step Explanation<\/h3>\n\n\n\n
\n\n\n\nStep 1: Calculate the Total Interest<\/h3>\n\n\n\n
\n\n\n\nStep 2: Sum of the Digits (Rule of 78)<\/h3>\n\n\n\n
\n\n\n\nStep 3: Calculate Interest in the Last Month<\/h3>\n\n\n\n
\n\n\n\nCorrect Approach: Rule of 78 with Flat Interest<\/h3>\n\n\n\n
\n\n\n\nFinal Answer<\/h3>\n\n\n\n