{"id":193519,"date":"2025-02-19T19:05:14","date_gmt":"2025-02-19T19:05:14","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=193519"},"modified":"2025-02-19T19:05:16","modified_gmt":"2025-02-19T19:05:16","slug":"you-place-a-deposit-for-91-days-at-11-5-on-an-act-360-basis","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/02\/19\/you-place-a-deposit-for-91-days-at-11-5-on-an-act-360-basis\/","title":{"rendered":"You place a deposit for 91 days at 11.5% on an ACT\/360 basis"},"content":{"rendered":"\n

You place a deposit for 91 days at 11.5% on an ACT\/360 basis. What would the rate have been if it had been quoted on an ACT\/365 basis? What is the effective yield on an ACT\/365 basis and on an ACT\/360 basis?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Answer:<\/h3>\n\n\n\n

To convert the interest rate from an ACT\/360<\/strong> basis to an ACT\/365<\/strong> basis, we use the following formula: r365=r360\u00d7360365r_{365} = r_{360} \\times \\frac{360}{365}<\/p>\n\n\n\n

Given that r360=11.5%r_{360} = 11.5\\%: r365=11.5%\u00d7360365r_{365} = 11.5\\% \\times \\frac{360}{365} r365=11.5%\u00d70.9863r_{365} = 11.5\\% \\times 0.9863 r365\u224811.34%r_{365} \\approx 11.34\\%<\/p>\n\n\n\n

Effective Yield Calculation:<\/h4>\n\n\n\n

The effective yield<\/strong> accounts for compounding and is calculated using the formula: Effective Yield=(1+r\u00d7tdenominator)\u22121\\text{Effective Yield} = \\left(1 + \\frac{r \\times t}{\\text{denominator}}\\right) – 1<\/p>\n\n\n\n

For ACT\/360<\/strong>: Effective Yield360=(1+0.115\u00d791360)\u22121\\text{Effective Yield}_{360} = \\left(1 + \\frac{0.115 \\times 91}{360}\\right) – 1 =(1+0.02906)\u22121= \\left(1 + 0.02906\\right) – 1 =2.91%= 2.91\\%<\/p>\n\n\n\n

For ACT\/365<\/strong>: Effective Yield365=(1+0.1134\u00d791365)\u22121\\text{Effective Yield}_{365} = \\left(1 + \\frac{0.1134 \\times 91}{365}\\right) – 1 =(1+0.02828)\u22121= \\left(1 + 0.02828\\right) – 1 =2.83%= 2.83\\%<\/p>\n\n\n\n

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

Interest rates in finance are quoted based on different day count conventions. The ACT\/360<\/strong> method assumes a 360-day year, which is common in money markets and banking, whereas the ACT\/365<\/strong> method considers the actual number of days in a year, typically used in government securities and bonds.<\/p>\n\n\n\n

Since ACT\/360 uses fewer days in the denominator, it results in a higher annualized interest rate<\/strong> compared to ACT\/365. To convert from ACT\/360 to ACT\/365, we adjust the rate by multiplying by 360365\\frac{360}{365}, leading to a slightly lower rate.<\/p>\n\n\n\n

The effective yield<\/strong> represents the actual return over the period. Since ACT\/360 assumes a shorter year, it results in a slightly higher effective yield compared to ACT\/365. In this case, the effective yield on an ACT\/360 basis is 2.91%<\/strong>, while on an ACT\/365 basis, it is 2.83%<\/strong>.<\/p>\n\n\n\n

This distinction is crucial in financial calculations as it impacts interest earnings, loan costs, and return on investments.<\/p>\n\n\n\n

I’ve generated a financial chart comparing ACT\/360 and ACT\/365 interest rate calculations. The image visually represents the formulas, effective yields, and the differences between both methods. Let me know if you need any modifications or further explanations!<\/p>\n\n\n\n

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

You place a deposit for 91 days at 11.5% on an ACT\/360 basis. What would the rate have been if it had been quoted on an ACT\/365 basis? What is the effective yield on an ACT\/365 basis and on an ACT\/360 basis? The correct answer and explanation is: Answer: To convert the interest rate from […]<\/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-193519","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193519","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=193519"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/193519\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=193519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=193519"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=193519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}