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The sheet also summarizes annuity variants and spot and forward rate structures to support exam practice and problem solving.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/actex-learning-exam-cm-1-formula-review-sheet/398872/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/actex-learning-exam-cm-1-formula-review-sheet/398872.png","ImageObject",300,407,{"name":42,"@type":43},"Guten tag","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-28","2026-09-27",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",10,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What topics does the CM 1 formula and review sheet cover?","Question",{"text":63,"@type":64},"It covers the time value of money, cashflow valuation (discrete and continuous), annuities (immediate, due, continuous, and p-thly), perpetuities, deferred annuities, increasing annuities, and term structure concepts including spot and forward rates.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are accumulation and discount factors related in the sheet?",{"text":68,"@type":64},"It lists accumulation factors A(t1,t2), simple and compound interest relationships, present value factors for v, and links between effective interest rate i, discount rate d, and force of interest δ.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the sheet value cashflows?",{"text":72,"@type":64},"It gives valuation expressions for discrete cashflows using sums of c_j v(t_j) and for continuously payable cashflows using integrals of v(t)ρ(t)dt, including formulas for payment rates and cumulative payments.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},398872,1790578990,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":55,"slug":125},"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":127,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":144,"preview_page_count":4},687212321768,"https://ap-avatar.wpscdn.com/avatar/a0010bdbe886d2fe77?x-image-process=image/resize,m_fixed,w_180,h_180&k=1789897067658708522","Formula & Review Sheet for Exam CM1  \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  \nexperience. Our complete study program is designed to help you understand concepts, practice effectively, and pass with confidence.  \nWith the ACTEX Learning Bundle for Exam CM1, you get:  \n Core Readings  \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 One-On-One Tutoring  \nLearn More  \nClick anywhere on this page or scan the QR code to learn more about offerings for this exam.  \nACTEX Learning  \nExam CM1 Formula & Review Sheet  \n(updated 10/29/2024)  \nTIME VALUE OF MONEY  \nAccumulation Factor A (t1 , t2 ) : The accumulation at time t2 of an investment of 1 at time t 1 for t 1 \u003C t2 ,  \nA (n) = A(0, n)  \nSimple Interest:  \nCompound Interest:  \nPresent Value Factor:  \nEffective Interest Rate:  \nEffective Discount Rate:  \nSimple Discount:  \nEffective Discount:  \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:  \nPrinciple of Consistency:  \nA (n) = C(1 + in)  \nA (n) = C(1 + i)n  \n 1  v (n) =  \nA (n) A (n) − A(n − 1)  \nin =  \nA (n − 1)  \nA (n) − A(n − 1) dn =  \nA (n) C(1 − nd)  \nC(1 − d)n  i   \nd = = 1 − v = iv  \n1 + i  \n( 1 + i~~ ~~(pp) )p = 1 + ii (p) = p [(1 + i)~~1~~p − 1]δt = VV′~~t~~t = ddt ln Vt  \nin = i  \nv = (1 + i)−1  \n( 1 − dp(p))p = 1 − dd (p) = p [ 1 − (1 − d)~~1~~p ] A (t1 , t2 ) = e∫tt21 δtdr  \n1d − 1i = 1  \nA(0, n) = e∫0n δdt = eδn  \neδ = 1 + i δ = ln(1 + i) v = e −δ  \nPV = (1 + i)−t = vt = e −δt = (1 − d)t = ( 1 + i~~ ~~(mm) ) −mt = ( 1 − dm(m))mt AV = (1 + i)t = eδt = (1 − d)−t = ( 1 + i~~ ~~(mm) )mt = ( 1 − dm(m)) −mt  \nA (t0 , tn ) = A (t0 , t 1 ) A (t1 , t2 ) . . . A (tn−1, tn)  \nCASHFLOWS  \nDiscrete cashflows: ct1 v (t1 ) + ct2 v (t2 ) + · · · + ctnv (tn ) = 1 ctj v (tj)  \n ctj v (tj), if the No. of payments is infinite  \nρ (t): The rate of payment at time t per unit time.  \nM (t): The total payment made between time 0 and time t  \nContinuously payable cashflows:  \nρ (t) = M′(t) for all t  \nThe payment received between time α and time β :  \nM (β) − M(α) =∫βα M′(t)dt = ∫βα ρ (t)dt where 0 ≤ α \u003C β ≤ T  \nPV of the entire cashflow: ∫0T v (t)ρ (t)dt ∫0∞ v (t)ρ (t)dt, if the No. of payments is infinite  \n[www.ACTEXLearning.com](www.ACTEXLearning.com)  \n Need Help? Email [support@actexlearning.com](support@actexlearning.com)  \nCopyright © ArchiMedia Advantage Inc. All Rights Reserved  \nACTEX Learning Exam CM 1 Formula & Review Sheet 2  \nGeneral Cashflow: ∑ ctv (t)+ ∫0∞ v (t)ρ (t)dt  \nValue at time t1 of C due at time t2 : C exp [−∫tt12 δ (t)dt] and∫tt12 δ (t)dt = ∫t02 δ (t)dt −∫t01 δ (t)dt  \nValuing cashflows: ∑ ctv (t) +∫ ρ (t)v (t)dt  \n􀀲􀀴 Valuofecaasthtflimowe t 1􀀳􀀵 = 􀀲􀀴 Valuofecaasthtflimowe t2􀀳􀀵 [ vv~~ ~~((t~~ ~~2t~~ ~~1)) ]􀀲􀀴 Vaolfuecaat timshflowe t􀀳􀀵 = 􀀲􀀴 Vatliuemeatofthceasprhfleosewnt 􀀳􀀵 [ v~~ ~~1(t)]  \nInterest income: I (T ) =∫0T Cδ (t)dt  \nCapital C: C = C∫0T δ (t)v (t)dt + Cv(T )  \nANNUITY  \nAnnuity-Immediate: an : one period before first payment, sn : at time of last payment  \na~~n~~ = v + v 2 + · · · + vn = 1~~ ~~vn  \ns~~n~~ = 1 + (1 + i) + · · · + (1 + i)n−1 = (1~~ ~~+~~ ~~ii)n~~ ~~−~~ ~~1 = a~~n~~ (1 + i)n  \nAnnuity-Due: a¨n : at time of first payment, s¨n : one period after last payment  \na¨~~n~~ = 1 + v + · · · + vn−1 = 1~~ ~~vn = (1 + i)a~~n~~ = ( id) a~~n~~ = 1 + an−1~~  ~~s¨~~n~~ = (1 + i) + (1 + i)2 + · · · + (1 + i)n = (1~~ ~~+~~ ~~id)n~~ ~~−~~ ~~1 = a¨~~n~~ (1 + i)n  \n= (1 + i)s~~n~~ = ( id) s~~n~~ = sn+1 − 1  \nContinuous Annuity: a¯~~n~~ = 1~~ ~~vn = ( iδ) a~~n~~ = ∫0n e −δt","cbCaigUZfxDUg2WC","https://ap.wps.com/l/cbCaigUZfxDUg2WC","pdf",633514,"English","# Time Value of Money\n## Cashflows\n## Annuity\n## Term Structure of Interest Rates","[{\"question\":\"What topics does the CM 1 formula and review sheet cover?\",\"answer\":\"It covers the time value of money, cashflow valuation (discrete and continuous), annuities (immediate, due, continuous, and p-thly), perpetuities, deferred annuities, increasing annuities, and term structure concepts including spot and forward rates.\"},{\"question\":\"How are accumulation and discount factors related in the sheet?\",\"answer\":\"It lists accumulation factors A(t1,t2), simple and compound interest relationships, present value factors for v, and links between effective interest rate i, discount rate d, and force of interest δ.\"},{\"question\":\"How does the sheet value cashflows?\",\"answer\":\"It gives valuation expressions for discrete cashflows using sums of c_j v(t_j) and for continuously payable cashflows using integrals of v(t)ρ(t)dt, including formulas for payment rates and cumulative payments.\"}]","ACTEX Learning Exam CM 1 - Formula & Review Sheet | PDF",1790489441,48]