[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207757-en":3,"doc-seo-207757-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},207757,2336474466712,"Quinn Holloway","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",4,"Exam","Applications 6.1 AER and compound interest - calculation practice","Covers how to apply compound interest concepts to real investment scenarios, focusing on the annual equivalent rate (AER) and interest compounding across multiple years or within different payment intervals. Includes learning objectives, key-point definitions of compound interest and AER, the standard value formula V=P(1+r/100)^n, and the method for deriving AER using nth roots. Provides worked examples and practice questions involving calculating final values, total interest, tax on interest, and determining required initial amounts or interest rates.","Applications 6.1 AER and compound interest  \nA6.1 AER and compound interest  \n\n| \u003Cbr> Before you start | \u003Cbr> Why do this? |\n| --- | --- |\n|  You should already know how to increase an | Compound interest and the annual equivalent |\n| amount by a given percentage. | rate (AER) play an important role in everyday |\n|  You will need to be able to use your calculator to | investments, especially those taking place over |\n| find the nth root of a number. | more than two or three years. |\n| \u003Cbr> Objectives | \u003Cbr>Get Ready |\n|  Be able to calculate the final amount and the | 1 £6000 is invested at 4% p. a. Work out the value |\n| interest on an investment. | of the investment after one year. |\n|  Be able to calculate the annual equivalent rate | 2 Use a calculator to work out: |\n| (AER) of an investment. | a 210 b 6000 􀀓 (1 􀀑  )5\u003Cbr>__1\u003Cbr>3 Use a calculator to work out 7296 |\n\nKey Points  \n Compound interest is interest paid on the amount and the interest already earned.  \nKatie invests £3000 at 3 .4% compound interest. Work out the value of her investment after 2 years. Interest after 1 year 􀀕 _. 􀀕 £102  \nValue after 1 year 􀀕 investment 􀀑 interest after 1 year  \nValue after 1 year 􀀕 3000 􀀑 102 􀀕 £3102 Interest in year 2 􀀕 _1__0_. 􀀕 £105.47  \nValue after 2 years 􀀕 3102 􀀑 105.47 􀀕 £3207.47  \nValue after 2 years 􀀕 value after 1 year 􀀑 interest in year 2  \n1  Jim invests £2000 at 3% p. a. compound interest for 2 years. Work out the final amount.  \n 2  Jade invests £1500 at 3% compound interest for 10 years. Work out the final amount.  \nC  \nKey Points  \n Compound interest can also be calculated using a formula.  \n When £P is invested in an account paying r% compound interest per annum (p. a. ), the value, £V, of the investment after n years is given by:  \nV 􀀕 P (1 􀀑 )n  \n When £P is invested in an account for n years to produce an investment of value £V, the annual equivalent rate of interest (AER) is given by:  \n􀁁 􀀕 100 (() 􀀒1 ) where () 􀀕 n√  \n1  \nChapter 6 Financial and business applications  \nKatie invests £3000 at 3 .4% compound interest. Work out the value of her investment after 5 years.  \n􀀑 )5 􀀕 3000 􀀓 1.0345 􀀕 £3545.88  \nJosh invested £5000 in an account.  \nAfter 5 years the value of the account was £7000.  \nWork out the annual equivalent rate (AER) of the account.  \n􀁁 􀀕 100 􀀓 (() 􀀒1) 􀀕 100 􀀓 ( 1.4 􀀒1) 􀀕 6.96%  \nAdam invested some money into an account which paid interest annually. In the first year the account paid 2% compound interest.  \nIn the second year the account paid 4% interest,  \nand in the third year the account paid 6% interest.  \nWork out the annual rate of interest (AER) of the account.  \nV 􀀕 P ( 1 􀀑 ) ( 1 􀀑 ) ( 1 􀀑 ) 􀀕 1.124 448 P  \nUse the AER formula with n 􀀕 3 and V 􀀕 1.124 448P  \nAER 􀀕 100 􀀓 ((_.) 􀀒1) 􀀕 100 􀀓 ( 1.124448 􀀒1) 􀀕 3.99%  \nNBAs a way of checking, Adam’s investment should give the same return as if he had invested in an account paying 3.99% p.a. compound interest for 3 years  \nP 􀀓 (1 􀀑 .)3 􀀕 1.1245… 􀀓 P  \nwhich compares well with the 1.124448P above, the difference being dueto the rounding of the AER to 2 decimal places.  \nHolly invests £10000 in an account with an annual equivalent rate AER of 5% . She gets the interest paid half yearly. Work out the value of her first half yearly interest payment. Suppose her half yearly interest payment rate is x%, then:  \n(1 􀀑  )2 􀀕 (1 􀀑  )  \nSo: 1 􀀑  􀀕 √ x 􀀕 100 􀀓 (√ 􀀒 1) 􀀕 2.469 5 %  \nThis line comes from using compound interest for two successive half years and se􀀞ing it equal to using 5% for 1 year. This line will be true no ma􀀞er how much money is invested.  \nThe amount of money added to the account is £10 000 􀀓 2.469 5 % 􀀕 £246.95.  \n2  \nApplications 6.1 AER and compound interest  \n1  Work out the value of these investments in accounts paying annual compound interest after the number of years stated.  \n\n|  | Initial Investment | Annual Interest rate | Number of years |\n| --- | --- | --- | --- |\n| a | £5000 | 5% | 3 |\n| b | £2000 | 4% | 5 |\n| c | £500 | 3.5% | 6 |\n","cbCaitcyx6oT2D2x","https://ap.wps.com/l/cbCaitcyx6oT2D2x","pdf",437229,1,8,"English","en",105,"# Applications 6.1 AER and compound interest\n## Compound interest and AER overview\n## Key formulas and worked examples\n## Practice questions (investments and AER)","[{\"question\":\"What is compound interest in the context of this section?\",\"answer\":\"Compound interest is interest paid on the original amount plus interest already earned from previous periods.\"},{\"question\":\"How is the final value of an investment calculated with annual compound interest?\",\"answer\":\"The value after n years is given by V = P(1 + r/100)^n, where P is the initial investment and r is the annual interest rate.\"},{\"question\":\"What does AER mean and how is it used?\",\"answer\":\"AER is the annual equivalent rate of interest, allowing comparisons by converting a given compounding pattern into an equivalent annual compound interest rate.\"}]","Applications 6.1 AER and compound interest - calculation practice | PDF",1788601064,20,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"applications-61-aer-and-compound-interest-calculation-practice","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/applications-61-aer-and-compound-interest-calculation-practice/207757/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-08","2026-09-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is compound interest in the context of this section?","Question",{"text":75,"@type":76},"Compound interest is interest paid on the original amount plus interest already earned from previous periods.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is the final value of an investment calculated with annual compound interest?",{"text":80,"@type":76},"The value after n years is given by V = P(1 + r/100)^n, where P is the initial investment and r is the annual interest rate.",{"name":82,"@type":73,"acceptedAnswer":83},"What does AER mean and how is it used?",{"text":84,"@type":76},"AER is the annual equivalent rate of interest, allowing comparisons by converting a given compounding pattern into an equivalent annual compound interest rate.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,104,109,114,119,123,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":102,"slug":103},70,"exam",{"id":105,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":120,"show_sort_weight":121,"slug":122},"Research & Report",30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":29,"slug":126},9,"Religion & Spirituality","religion-spirituality",{"id":29,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":29,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":105,"slug":137},19,"General","general"]