[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657242-105":59,"doc-detail-657242-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","chapter-2-factors-how-time-and-interest-affect-money","Chapter 2 - Factors: How Time and Interest Affect Money","","Chapter 2 explains how engineering economy factors incorporate the time value of money for cash flows. It establishes single-payment relationships using compound amount and present worth factor formulas for future value and present value. The chapter defines the standard notation (X−Y, i, n) for identifying given versus sought quantities and interest and period inputs. It also covers how to compute factor values using formulas or interpolation and how spreadsheet functions (FV and PV) support equivalency calculations.",{"@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":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/chapter-2-factors-how-time-and-interest-affect-money/657242/",{"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/chapter-2-factors-how-time-and-interest-affect-money/657242.png","ImageObject",300,407,{"name":92,"@type":93},"RuangKosong","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of engineering economy factors in this chapter?","Question",{"text":112,"@type":113},"The purpose is to use engineering economy factors to account for the time value of money in cash flow problems.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the single-payment compound amount factor and present worth factor used?",{"text":117,"@type":113},"The compound amount factor converts a present amount P to a future amount F after n periods, while the present worth factor converts a future amount F back to its present worth P.",{"name":119,"@type":110,"acceptedAnswer":120},"How can factor values be obtained when interest rates or periods are not listed in the tables?",{"text":121,"@type":113},"They can be obtained using the derived formulas or by linearly interpolating between the tabulated factor values.","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},657242,1792976254,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":56,"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":129,"read_time":143},962090883219,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| \u003Cbr>\u003Cbr>\u003Cbr>C h a p t er |  2 |\n| --- | --- |\n| Factors: How Time and Interest Affect Money\u003Cbr>\u003Cbr>The McGraw-Hill Companies, Inc./John Flournoy\u003Cbr>n Chapter 1 we learned the basic concepts of engineering economy and their\u003Cbr>sroiesliht creisiuonnifmakorm,ign.dTiceasshthwinsredameor daroseevberyycecoonstomicnt amudyunts.\u003Cbr>Cash flows occur in many configurations and amounts—isolated single values,\u003Cbr>or constant percentages. This chapter develops the commonly used engineering economy factors that consider the time value of money for cash flows.\u003Cbr>The application of factors is illustrated using their mathematical forms and a standard notation format. Spreadsheet functions are illustrated. | \u003Cbr>27 |\n\n28  \nObjectives  \nPurpose: Use engineering economy factors to account for the time value of money.  \n1. Use the compound amount factor and present worth factor for single payments.  \n2. Use the uniform series factors.  \n3. Use the arithmetic gradient factors and the geometric gradient formula.  \n4. Use uniform series and gradient factors when cash flows are shifted.  \n5. Use a spreadsheet to make equivalency calculations.  \n2. 1 Single-Payment Formulas (F/P and P/F) 29  \n2.1 SINGLE-PAYMENT FORMULAS ( F/ P AND P/ F )  \nThe most fundamental equation in engineering economy is the one that determines the amount of money F accumulated after n years (or periods) from a single present worth P, with interest compounded one time per year (or period) . Recall that compound interest refers to interest paid on top of interest. Therefore, if an amount Pis invested at time t 􀀃 0, the amount F1 accumulated 1 year hence at an interest rate of i percent per year will be  \nF1 􀀃 P 􀀂 Pi  \n􀀃 P (1 􀀂 i)  \nwhere the interest rate is expressed in decimal form. At the end of the second year, the amount accumulated F2 is the amount after year 1 plus the interest from the end of year 1 to the end of year 2 on the entire F1.  \nF2 􀀃 F1 􀀂 F1i  \n􀀃 P (1 􀀂 i) 􀀂 P (1 􀀂 i)i  \nThe amount F2 can be expressed as  \nF2 􀀃 P (1 􀀂 i 􀀂 i 􀀂 i2)  \n􀀃 P (1 􀀂 2i 􀀂 i2)  \n􀀃 P (1 􀀂 i)2  \nSimilarly, the amount of money accumulated at the end of year 3 will be  \nF3 􀀃 P (1 􀀂 i)3  \nBy mathematical induction, the formula can be generalized for n years to  \nF 􀀂 P(1 􀀃 i)n [2.1]  \nThe term (1 􀀂 i)n is called a factor and is known as the single-payment compound amount factor (SPCAF), but it is usually referred to as the F􀀂P factor. This is the conversion factor that yields the future amount F of an initial amount P after n years at interest rate i. The cash flow diagram is seen in Figure 2.1a.  \nReverse the situation to determine the P value for a stated amount F. Simply solve Equation [2.1] for P.  \n 1   \nP 􀀂 Fc (1 􀀃 i)n d [2.2]  \nThe expression in brackets is known as the single-payment present worth factor (SPPWF), or the P􀀂Ffactor. This expression determines the present worth P of a given future amount F after n years at interest rate i. The cash flow diagram is shown in Figure 2.1b.  \nNote that the two factors derived here are for single payments; that is, they are used to find the present or future amount when only one payment or receipt is involved.  \n30 Chapter 2 Factors: How Time and Interest Affect Money  \nP = given  \nF = ?(a)  \nP = ?  \nF = given (b)  \nFIGURE 2.1 Cash flow diagrams for single-payment factors: (a) find F and (b) find P.  \nA standard notation has been adopted for all factors. It is always in the general form (X􀀂 Y,i,n) . The letter X represents what is sought, while the letter Y represents what is given. For example, F􀀂P means find F when given P. The i is the interest rate in percent, and n represents the number of periods involved. Thus,(F􀀂P,6%,20) represents the factor that is used to calculate the future amount F accumulated in  \n20 periods if the interest rate is 6% per period. The P is given. The standard notation, simpler to use than formulas and factor names, will be used hereafter. Table 2.1 summarizes the standard notation and equations for the F􀀂P and P􀀂F factors.","cbCainfKpHVB0fzc","https://ap.wps.com/l/cbCainfKpHVB0fzc","pdf",707723,"English","# Objectives\n## Single-Payment Formulas (F/P and P/F)\n## Standard Notation and Factor Tables\n## Spreadsheet Use (FV and PV)\n## Example 2.1","[{\"question\":\"What is the purpose of engineering economy factors in this chapter?\",\"answer\":\"The purpose is to use engineering economy factors to account for the time value of money in cash flow problems.\"},{\"question\":\"How are the single-payment compound amount factor and present worth factor used?\",\"answer\":\"The compound amount factor converts a present amount P to a future amount F after n periods, while the present worth factor converts a future amount F back to its present worth P.\"},{\"question\":\"How can factor values be obtained when interest rates or periods are not listed in the tables?\",\"answer\":\"They can be obtained using the derived formulas or by linearly interpolating between the tabulated factor values.\"}]","Chapter 2 - Factors: How Time and Interest Affect Money | PDF",48]