{"id":236794,"date":"2025-06-16T14:09:23","date_gmt":"2025-06-16T14:09:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236794"},"modified":"2025-06-16T14:09:25","modified_gmt":"2025-06-16T14:09:25","slug":"find-the-interest-refund-on-a-31-month-loan-with-interest-of-2-comma-790-if-the-loan-is-paid-in-full-with-8-months-remaining","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/find-the-interest-refund-on-a-31-month-loan-with-interest-of-2-comma-790-if-the-loan-is-paid-in-full-with-8-months-remaining\/","title":{"rendered":"Find the interest refund on a 31-month loan with interest of $2 comma 790 if the loan is paid in full with 8 months remaining."},"content":{"rendered":"\n

Find the interest refund on a 31-month loan with interest of $2 comma 790 if the loan is paid in full with 8 months remaining.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the interest refund, we use the Rule of 78s<\/strong>, a method often used to calculate interest refunds on loans paid off early.<\/p>\n\n\n\n

Step-by-step Solution:<\/strong><\/h3>\n\n\n\n

1. Total number of months in the loan:<\/strong>
31 months<\/p>\n\n\n\n

2. Interest paid originally:<\/strong>
$2,790<\/p>\n\n\n\n

3. Months remaining when loan is paid off:<\/strong>
8 months<\/p>\n\n\n\n

4. Months already paid:<\/strong>
31 \u2212 8 = 23 months<\/p>\n\n\n\n

5. Sum of the digits from 1 to 31 (known as the sum of the digits or \u201csum of months\u201d):<\/strong>
This is found using the formula:Sum=n(n+1)2=31(32)2=496\\text{Sum} = \\frac{n(n + 1)}{2} = \\frac{31(32)}{2} = 496Sum=2n(n+1)\u200b=231(32)\u200b=496<\/p>\n\n\n\n

6. Sum of the remaining months\u2019 digits (for refund):<\/strong>
Add up digits from month 1 to month 8:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36<\/p>\n\n\n\n

7. Proportion of interest to be refunded:<\/strong>36496\\frac{36}{496}49636\u200b<\/p>\n\n\n\n

8. Refund amount:<\/strong>Refund=36496\u00d72790=202.5\\text{Refund} = \\frac{36}{496} \\times 2790 = 202.5Refund=49636\u200b\u00d72790=202.5<\/p>\n\n\n\n

\u2705 Final Answer:<\/strong><\/h3>\n\n\n\n

$202.50<\/strong><\/p>\n\n\n\n

\n\n\n\n

Explanation:<\/strong><\/h3>\n\n\n\n

When a loan is paid off early, the borrower is entitled to a refund of the unused portion of the interest. The Rule of 78s assumes that interest is paid more heavily in the earlier months of the loan. Each month is assigned a number from the total term down to 1, and those are added to find the total \u201cweight\u201d of interest payments. The earlier payments carry more weight, which is why the refund for unused months is less than a simple proportional calculation.<\/p>\n\n\n\n

In this case, with 8 months left, the remaining months represent a smaller portion of the total interest weight. By applying the correct proportion using the Rule of 78s, we calculated the refund to be $202.50. This ensures fairness in the amount of interest retained versus returned.<\/p>\n\n\n\n

\"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

Find the interest refund on a 31-month loan with interest of $2 comma 790 if the loan is paid in full with 8 months remaining. The Correct Answer and Explanation is: To find the interest refund, we use the Rule of 78s, a method often used to calculate interest refunds on loans paid off early. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-236794","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=236794"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236794\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}