[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-399164-105":59,"doc-detail-399164-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","digital-actuarial-resources-equation-guide-society-of-actuaries-exam-fm-financial-mathematics","Digital Actuarial Resources Equation Guide - Society of Actuaries Exam FM Financial Mathematics","","Comprehensive equation guide for Society of Actuaries Exam FM (Financial Mathematics), intended to support preparation beginning in spring 2005. Provides 180+ organized formulas covering theory of interest topics such as compound interest, annuities, cash flows, loans, bonds, and stocks. Includes introductory interest, simple and compound interest/discount, nominal rates compounded per year, force of interest, short-term interest forms, and linear interpolation for unknown rates. Includes index-based navigation and notes that not all exam material is guaranteed to be covered.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/digital-actuarial-resources-equation-guide-society-of-actuaries-exam-fm-financial-mathematics/399164/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/digital-actuarial-resources-equation-guide-society-of-actuaries-exam-fm-financial-mathematics/399164.png","ImageObject",300,407,{"name":92,"@type":93},"Eliana","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What exam and subject area does this equation guide support?","Question",{"text":112,"@type":113},"It is designed for Society of Actuaries Exam FM (Financial Mathematics) and covers theory of interest topics included on the exam.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How is the content organized for study?",{"text":117,"@type":113},"The guide contains 180+ formulas neatly organized into multiple categories and an index is provided to help locate topics.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the guide guarantee coverage of all Exam FM materials?",{"text":121,"@type":113},"No. It states the list is not guaranteed to cover all material on the exam, and equations unlikely to appear are excluded.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},399164,1791077246,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},4398048949847,"https://ap-avatar.wpscdn.com/avatar/400002536579ef2da7f?_k=1778318612642679267","1  \nDigital Actuarial Resources Equation Guide (Sample)  \nSociety of Actuaries Exam FM: Financial Mathematics  \nIntroduction:  \nThis compilation of equations is designed to aid the student in preparing for Exam FM (Financial Mathematics) offered through the Society of Actuaries starting in the spring of 2005. The comprehensive list contains equations for most of the theory of interest subjects that the exam covers. This formula sheet includes topics from compound interest to annuities to stocks. The list is not guaranteed to cover all the material that exists on the exam. Equations that are unlikely to show up on an exam are not included in this compilation. The 180+ formulas are neatly organized into several categories. Refer to the index for guidance.  \nCopyright 2005  \n[www.digitalactuarialresources.com](www.digitalactuarialresources.com)  \nDigital Actuarial Resources, Exam FM Guide  \n2  \nIndex  \nSection 1: Introductory Interest Equations …………………………………3  \nSection 2: Annuities ………………………………………………………….. 6  \nSection 3: Cash Flows ………….…………………………………………….. 10  \nSection 4: Loans …..………………………………………………………….. 12  \nSection 5: Bonds …..………………………………………………………….. 13  \nSection 6: Stocks …..………………………………………………………….. 17  \nSection X: Other Mathematical Equations ...……………………………….. 18  \nDigital Actuarial Resources, Exam FM Guide  \n3  \nSection 1: Introductory Interest Equations  \na(t ) = accumulation function  \nA(t) = k * a(t) = amount function  \nIn = A(n) − A(n −1) = interest earned in nth period  \nin = ~~ ~~A(nA)~~ ~~−(n(n1)−1) = ~~ ~~a(na)~~ ~~a−(n1)−1) = effective rate of interest during nth period d =  A(n) − A(n −1) = a(n) − a(n −1) effective rate of discount during nth period n A(n) a(n)  \nv = (1 + i) −1  \nv n = (1+ i) −nd = i~~ ~~~~ ~~1 = iv  \nv + d = 1  \n(1− d)(1+ i) = 1  \nd = 1 − v  \ni − d = id  \nSimple Interest:  \ni = annual rate of simple interest  \nt = number of years  \nac.v. = a(t ) = 1 + i * t  \np.v. = a −1 (t ) = (1 + i *t) −1 Simple Discount:  \nd = annual rate of simple discount  \nt = number of years  \nac.v. = a(t ) = (1 − d * t) −1  \np.v. = a −1 (t ) = 1 − d * t  \nDigital Actuarial Resources, Exam FM Guide  \n4  \nCompound Interest:  \ni = annual effective rate of interest  \nac.v. = a(t ) = (1 + i) t  \np.v. = a −1 (t ) = (1 + i) −t = vt Compound Discount:  \nd = annual effective rate of discount  \nac.v. = a(t ) = (1 − d) −t  \np.v. = a −1 (t ) = (1 − d) t = vt  \nNominal, Compound Interest:  \ni (m) = nominal rate of interest compounded m times per year  \n1 + i = ⎜1 + ~~ ~~im(m)~~ ~~⎟ mac.v. = a(t ) = ⎜1 + ~~ ~~im(m)~~ ~~⎟mt p.v. = a −1 (t ) = ⎜1 + ~~ ~~im(m)~~ ~~⎟−mt  \nim(m)~~ ~~ = effective rate of interest per mth of a year dm(m)~~ ~~ = effective rate of discount per mth of a year  \nNominal, Compound Discount:  \nd (m) = nominal rate of discount compounded m times per year  \nd = 1 − ⎜1 − ~~ ~~dm(m)~~ ~~⎟ mac.v. = a(t ) = ⎜1 − ~~ ~~dm(m)~~ ~~⎟−mt  \nDigital Actuarial Resources, Exam FM Guide  \n5  \np.v. = a −1(t ) = ⎜1 − ~~ ~~dm(m)~~ ~~⎟mt Force of Interest:  \nδt = ~~ ~~AA'()) = ~~ ~~aa'()) = force of interest  \nIf δ is a constant, then a(t ) = e δt  \nt  \n∫δr dr  \nIf δr is a function of r, then a(t ) = e0  \ne δ = 1 + i , δ = ln(1 + i)  \nForms of Short-Term Interest:  \nExact Simple Interest: exact number days, 365 days per year  \nOrdinary Simple Interest: each month has 30 days, 360 days per year  \nBanker’s Rule: exact number of days, 360 days per year  \nLinear Interpolation:  \n*Use for finding an unknown rate of interest ( j )  \n* j1 = first rate of interest  \n* j2 = second rate of interest  \n* ∆j = j2 − j1  \n* f ( j) = a function of j with one side of the equation set to 0  \n*Must solve for j (the unknown rate of interest) that makes the equation true j = j1 + ∆j * ⎜ ~~ ~~f~~ ~~(−j~~ ~~2~~ ~~f)~~ ~~−(jf1~~ ~~)(j1~~ ~~)~~ ~~ ⎟  \nOther Equations:  \nFor compound interest, a(t + s) = a(t ) * a(s)  \ni (m) d (m) i (m) d (m)  \n  −   =   *   m m m m  \nIf the length of time is n + k, where n is an integer and 0\u003Ck\u003C1, use compound interest over t","cbCaijV2aw21r18T","https://ap.wps.com/l/cbCaijV2aw21r18T","pdf",127819,"English","# Introduction\n# Index\n## Section 1: Introductory Interest Equations\n## Section 2: Annuities\n## Section 3: Cash Flows\n## Section 4: Loans\n## Section 5: Bonds\n## Section 6: Stocks\n## Section X: Other Mathematical Equations\n# Section 1: Introductory Interest Equations\n# Simple Interest\n# Compound Interest\n# Force of Interest\n# Forms of Short-Term Interest\n# Linear Interpolation\n# Other Equations","[{\"question\":\"What exam and subject area does this equation guide support?\",\"answer\":\"It is designed for Society of Actuaries Exam FM (Financial Mathematics) and covers theory of interest topics included on the exam.\"},{\"question\":\"How is the content organized for study?\",\"answer\":\"The guide contains 180+ formulas neatly organized into multiple categories and an index is provided to help locate topics.\"},{\"question\":\"Does the guide guarantee coverage of all Exam FM materials?\",\"answer\":\"No. It states the list is not guaranteed to cover all material on the exam, and equations unlikely to appear are excluded.\"}]","Digital Actuarial Resources Equation Guide - Society of Actuaries Exam FM Financial Mathematics | PDF",1790494102,13]