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Covers time value of money with accumulation, discounting, effective and nominal rates, force of interest, and present/accumulated values. Includes annuities (immediate/due, continuous, deferred, perpetuities, and varying payments), geometric and arithmetic progression structures, and formulas using varying force of interest. Further provides structured loan amortization methods, bond pricing and book value relations, callable bond redemption logic, and general cash-flow reinvestment framing.",{"@graph":69,"@context":123},[70,84,106],{"@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/actex-learning-exam-fm-formula-review-sheet/398753/",{"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/actex-learning-exam-fm-formula-review-sheet/398753.png","ImageObject",300,407,{"name":92,"@type":93},"Mafia Boss","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What topics are covered in the Exam FM formula and review sheet?","Question",{"text":113,"@type":114},"It covers the time value of money, multiple annuity types and special progression forms, loan amortization methods, and bond pricing (including callable bonds) plus general cash-flow reinvestment rates.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the sheet treat interest in the time value of money section?",{"text":118,"@type":114},"It includes effective and nominal rates, simple and compound interest, discount rates, and force of interest, along with corresponding formulas for PV and accumulated value relationships.",{"name":120,"@type":111,"acceptedAnswer":121},"What does the sheet include for loans and bonds?",{"text":122,"@type":114},"For loans, it provides an amortization method with formulas for outstanding balance and principal/interest components. For bonds, it gives price formulas, callable bond pricing guidance using redemption date assumptions, and book value and interest earned relations.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},398753,1791102178,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},962090760730,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Formula & Review Sheet for Exam FM  \nYour quick-reference guide for the most important formulas and concepts you need.  \nWant More Than Just the Formula Sheet?  \nThis free Formula & Review Sheet is just one part of the ACTEX Learning experience. Our complete study program is designed to help you  \nunderstand concepts, practice effectively, and pass with confidence. With the ACTEX Learning Bundle for Exam FM, you get:  \n Comprehensive Study Manual  \n GOAL Practice Problems  \n Instructional Videos  \n Flashcards  \n Formula & Review Sheets  \n Learning Platform with a Study Planner and Topic Explorer  \nWant an Extra Edge?  \nTake your preparation even further with premium ACTEX resources designed to sharpen exam skills and boost confidence when it matters most.  \nPopular Upgrades:  \n Live Bootcamps  \n One-On-One Tutoring  Graded Mock Exams  \nLearn More  \nClick anywhere on this page or scan the QR code to learn more about offerings for this exam. ~~ ~~  \nExam FM Formula & Review Sheet  \n(updated 06/29/2023)  \nTIME VALUE OF MONEY  \nAccumulation and Amount Functions:  \nEffective Interest Rate:  \nSimple Interest:  \nCompound Interest:  \nEffective Discount Rate:  \nDiscount Rate:  \nNominal Rates:  \nForce of Interest:  \nConstant Force of Interest:  \nPV of $1 Due in t Years:  \nAV at time t of $1 invested at time 0:  \nAV at time t2 for $1 Invested at time t1 :  \nA (t) = Ka(t), A(0) = K , a(0) = 1  \na (t) 􀀀 a(t 􀀀 1)  A (t) 􀀀 A(t 􀀀 1)  \nit = =  \na (t 􀀀 1) A (t 􀀀 1)  \n i   \na (t) = 1 + it it =  \n1 + i(t 􀀀 1)  \na (t) = (1 + i)t it = i  \na (t) 􀀀 a(t 􀀀 1)  A (t) 􀀀 A(t 􀀀 1)  \ndt = a (t) = A (t)  \nd = 1~~ ~~~~ ~~i = 1 􀀀 v = iv v = (1 + i)􀀀1 ~~ ~~1d 􀀀 1i = 1  \n􀀒 1 + i~~ ~~(mm) 􀀓 m = 1 + i 􀀒 1 􀀀 dm(m) 􀀓 m = 1 􀀀 di (m) = m h (1 + i)~~1~~m 􀀀 1i d (m) = m h 1 􀀀 (1 􀀀 d)~~1~~m i  \n􀀎t = aa0((tt)) = AA0((tt)) = ddt ln a(t) a (t) = eRt0 􀀎r dre􀀎 = 1 + i 􀀎 = ln(1 + i)  \nPV = a~~ ~~1(t) = (1 + i)􀀀t = vt = e 􀀀􀀎t = (1 􀀀 d)t = 􀀒 1 + i~~ ~~(mm) 􀀓 􀀀mt = 􀀒 1 􀀀 dm(m) 􀀓 mt  \nAV = a (t) = (1+i)t = e􀀎t = (1􀀀d)􀀀t = 􀀒 1 + i~~ ~~(mm) 􀀓 mt = 􀀒 1 􀀀 dm(m) 􀀓 􀀀mt  \nAV = aa((t~~ ~~2t~~ ~~1)) = eRtt21 􀀎tdt  \nANNUITIES  \nAnnuity-Immediate:  \nAnnuity-Due:  \n(PV one period before first payment, AV at time of last payment) PV = a~~n~~ = v + v 2 + 􀀁 􀀁 􀀁 + vn = 1~~ ~~~~ ~~vn  \nAV = s~~n~~ = 1 + (1 + i) + 􀀁 􀀁 􀀁 + (1 + i)n􀀀1 = (1~~ ~~+~~ ~~ii)n~~ ~~􀀀~~ ~~1 = a~~n~~ (1 + i)n (PV at time of first payment, AV one period after last payment)  \nPV = ~~n~~ = 1 + v + 􀀁 􀀁 􀀁 + vn􀀀1 = 1~~ ~~vn = (1 + i)a~~n~~ = 􀀒 id􀀓 a~~n~~ = 1 + an􀀀1 AV = ~~n~~ = (1 + i) + (1 + i)2 + 􀀁 􀀁 􀀁 + (1 + i)n = (1~~ ~~+~~ ~~id)n~~ ~~􀀀~~ ~~1  \n= (1 + i)s~~n~~ = 􀀒 id􀀓 s~~n~~ = sn+1 􀀀 1  \nNeed Help? Email [support@actuarialuniversity.com](support@actuarialuniversity.com) Copyright © ArchiMedia Advantage Inc. All Rights Reserved  \nACTEX Learning  \nExam FM  \nPage 2  \nContinuous Annuity: PV = n = 1 vn = 􀀒 i􀀎 􀀓 an = R0n vtdt = R0n e 􀀀􀀎tdt  \nAV = n = (1 + i􀀎)n 􀀀 1 = 􀀒 i􀀎 􀀓 sn = R0n (1 + i)n􀀀tdt = R0n e􀀎 (n􀀀t)dt  \nDeferred Annuity: m jan = m+1j n = vman = am+n 􀀀 am  \n1 1 1  \nPerpetuity: a 1 = 1 = 1 =  \ni d 􀀎  \nIncreasing Annuity-Payments in Arithmetic Progression:  \n(Ia)n =  \n(I) n =  \nn 􀀀 nvni  \nn 􀀀 nvnd  \nDecreasing Annuity-Payments in Arithmetic Progression:  \n(Da)n (D) n  \nn 􀀀 an  \n=  \ni  \nn 􀀀 an  \n=  \nd  \nIncreasing Perpetuity-Payments in Arithmetic  \n1 1 (Ia)1 = i + i2 =  \n(m) 1 􀀀 vnm-thly Annuity: an = i (m)  \nProgression:  \n1 id  \n(Ia)n(m) = ni􀀀(mn) vn  \n(Is)n  \n(I) n  \nn 􀀀 n s n+1  \n= =  \ni  \nn 􀀀 n s n+1  \n= =  \nd  \n(Ds)n =  \n(D) n =  \n(I) 1 =  \nn(1 + i)n 􀀀 snin(1 + i)n 􀀀 snd  \n1 d2  \nn(m) = 1d􀀀(mv)n  \n(m) 􀀀 nvn (I(m)a)n(m) = n i (m)  \n􀀀 (n + 1) i  \n􀀀 (n + 1) d  \nContinuously Increasing  \nAnnuity:  \n􀀖(I) n  \n􀀖(I) n  \n=  \nn 􀀀  \n􀀎  \nnvn n n  \n= R0 tvtdt = R0 te 􀀀􀀎tdt  \n= n  n = R0n t(1 + i)n􀀀tdt = R0n te􀀎 (n􀀀t)dt  \nAnnuity with Varying Payments and Varying Force of Interest:  \nPV = R0n f (t)e 􀀀􀀎tdt If force of interest varies: PV = R0n f (t)e 􀀀Rt0 􀀎rdrdt AV = R0n f (t)e􀀎 (n􀀀t)dt If force of interest varies: FV = R0n f (t)eRtn 􀀎","cbCailZ4I6rZtcY0","https://ap.wps.com/l/cbCailZ4I6rZtcY0","pdf",1302885,"English","# TIME VALUE OF MONEY\n## Accumulation and Amount Functions\n## Discounting and Force of Interest\n## Present and Accumulated Values\n# ANNUITIES\n## Annuity-Immediate and Annuity-Due\n## Continuous and Deferred Annuities\n## Perpetuities and Increasing/Decreasing Annuities\n## Geometric Annuities and Varying Force of Interest\n# LOANS\n## Amortization Method\n# BONDS\n## Price Formulas\n## Callable Bonds\n## Book Value and Interest Earned\n# GENERAL CASH FLOW\n## Reinvestment Rates","[{\"question\":\"What topics are covered in the Exam FM formula and review sheet?\",\"answer\":\"It covers the time value of money, multiple annuity types and special progression forms, loan amortization methods, and bond pricing (including callable bonds) plus general cash-flow reinvestment rates.\"},{\"question\":\"How does the sheet treat interest in the time value of money section?\",\"answer\":\"It includes effective and nominal rates, simple and compound interest, discount rates, and force of interest, along with corresponding formulas for PV and accumulated value relationships.\"},{\"question\":\"What does the sheet include for loans and bonds?\",\"answer\":\"For loans, it provides an amortization method with formulas for outstanding balance and principal/interest components. For bonds, it gives price formulas, callable bond pricing guidance using redemption date assumptions, and book value and interest earned relations.\"}]","ACTEX Learning - Exam FM - Formula & Review Sheet | PDF",1790488680,13]