[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-207756-en":3,"doc-seo-207756-105":30,"detail-sidebar-cat-0-en-105":90},{"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":4,"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},207756,1099523885074,"Riley West","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc",4,"Exam","GCSE Maths - Ratio, Proportion and Rates of Change - Compound Growth and Decay - Notes and Practice Questions","GCSE Maths notes and practice questions on compound growth and compound decay, building from percentage change. The material defines growth as repeated percentage increase and shows how to model it with a formula using initial value, percentage rate, and number of periods. It contrasts compound decay with growth, then explains compound interest versus simple interest through worked examples. Practice questions cover population growth, repeated migration, depreciation of a car, and compound interest calculations, including interpreting results after multiple time periods.","# GCSE Maths – Ratio, Proportion andRates of Change\n\nCompound Growth and Decay  \nNotes  \nWORKSHEET  \nCompound Growth and Decay  \n## Growth\n\nGrowth is when an original value is increased by a percentage.  \nAn example is the pet health insurance sector for the United States. Gross premiums wereat $1.56 billion in 2019, and increased by 27.5% to reach $1.99 billion in 2020.  \nCompound interest is a common example of growth. We will learn how to calculatecompound interest later.  \nGrowth can be calculated using a formula:  \n􀡺 = 􀡺 􀫙 × 􀵬 􀫚 + 􀢔  \nN = amount after time period  \n􀡺 􀫙 = original amount  \nn = number of periods (this might be days / minutes / years)  \n\n| Example: The population of salmon in a fishery is 5000 , it increases by 10% eachyear. How many salmon will there be after 1 year? How many salmon after 5 years?   |\n| --- |\n| 1. Use the formula with n = 1.  \u003Cbr>N = population after 1 year, 􀜰0 = 5000, percentage = 10%􀜲􀝋􀝌􀝑􀝈􀜽􀝐􀝅􀝋􀝊 = 5000 × (1 + )  \u003Cbr>􀜲􀝋􀝌􀝑􀝈􀜽􀝐􀝅􀝋􀝊 = 􀫞􀫞􀫙􀫙 􀢙􀢇􀢒􀢓􀢕􀢔  \u003Cbr>2. Use the formula with n = 5.  \u003Cbr>N = population after 5 years, 􀜰0 = 5000, percentage = 10%􀜲􀝋􀝌􀝑􀝈􀜽􀝐􀝅􀝋􀝊 = 5000 × 􀵬 1 +  5  \u003Cbr>􀜲􀝋􀝌􀝑􀝈􀜽􀝐􀝅􀝋􀝊 􀜽􀝂􀝐􀝁􀝎 5 􀝕􀝁􀜽􀝎􀝏 = 8052.55 􀝏􀜽􀝈􀝉􀝋􀝊= 􀫡􀫙􀫞􀫜 􀢙􀢇􀢒􀢓􀢕􀢔 (􀝐􀝋 􀝐ℎ􀝁 􀝊􀝁􀜽􀝎􀝁􀝏􀝐 􀝓ℎ􀝋􀝈􀝁 􀝊􀝑􀝉􀜾􀝁􀝎)  \u003Cbr>The salmon population grew by 500 in the first year.  \u003Cbr>However, the population grew by different amounts each year dueto thechanging initial population.  \u003Cbr>For example, after the 2nd year, 􀝌􀝋􀝌􀝑􀝈􀜽􀝐􀝅􀝋􀝊 = 5500 × 􁉀 1 +  = 6050.This is an increase of 6050 − 5500 = 550 from year 1. This shows we cannotcontinually add n × 500 to find the population after n years.   |\n\n## Decay\n\nDecay is when an original value is decreased by a percentage.  \nCompound decay (depreciation) is when the percentage is deducted after each time period.Decay can be calculated using the formula, which is very similar to the formula for growth.  \n􀡺 = 􀡺 􀫙 × 􀵬 􀫚 − 􀢔  \nN = amount after time period  \n􀡺 􀫙 = original amount  \nn = number of periods (this might be days/ minutes/ years)  \n\n| Example: A new car is bought for £13,000 . It depreciated by 21% each yearfor 10 years. How much value is lost after 10 years (to the nearest pence)?   |\n| --- |\n| 1. Use the depreciation formula to find the value after 10 years.  \u003Cbr>􀜰0 = 13,000, n = 10, percentage = 21%  \u003Cbr>􀜰 = 13,000 × 􀵬 1 − 10  \u003Cbr>􀜰 = 1230.8758 …  \u003Cbr>􀜸􀜽􀝈􀝑􀝁 􀜽􀝂􀝐􀝁􀝎 10 􀝕􀝁􀜽􀝎􀝏 = £1230 .88  \u003Cbr>2. Calculate the value lost.  \u003Cbr>13000 – 1230.88 = £11,769.12  \u003Cbr>􀢂􀢇􀢒􀢛􀢋 􀢒􀢕􀢙􀢚 = £􀫚􀫚 , 􀫠􀫟􀫢 . 􀫚􀫛   |\n\n## Compound interest\n\nCompound interest is a form of compound growth.  \nSimple interest is where we increase an original value by a percentage.Compound interest occurs when the added interest then also receives interest insubsequent periods.  \n\n| Example: The compound interest rate at a bank 3% per year. Laureninvests £100 into the bank. How much is in her account after 3 years?   |\n| --- |\n| 1. Work this out year by year.  \u003Cbr>After 1st year: 100 × 1.03 = £103  \u003Cbr>After 2nd year: 103 × 1.03 = £106 .09  \u003Cbr>After 3rd year: 106.09 × 1.03 = £109 .27  \u003Cbr>Lauren has £109.27 in her account after 3 years  \u003Cbr>Interest is compounded annually; this is not the same as simpleinterest.  \u003Cbr>If using simple interest, we would find 3% of £100 = £3.  \u003Cbr>We would then add 3 x £3 to £100 = £109 after 3 years.  \u003Cbr>This is slightly less than the value found using compound interest,but for larger initial values the difference is more significant.  \u003Cbr>2. Alternatively, use the growth formula.  \u003Cbr>We can also calculate compound interest quickly using the growthformula.  \u003Cbr>􀜰0 = £100, n = 3, percentage = 3%  \u003Cbr>􀜰 = 100 × 􀵬 1 + 3 = £109 .27   |\n\n# Compound Growth and Decay - Practice Questions\n\n1. Red Squirrels are entering the UK at a rate of 5.2% a year. Currently there are 590red squirrels in the UK. What is the expected number red squirrels after 6 years?  \n2. UK retirees are migrating to holiday homes in Spain. Every year, 2.3% of UKresidents move to Spain. In 2021, there are 2700 UK retirees. How many retirees willthere be in 2027?  \n3. Wat","cbCaiuXyHNMjtcup","https://ap.wps.com/l/cbCaiuXyHNMjtcup","pdf",385346,1,5,"English","en",105,"# Growth\n## Decay\n## Compound interest\n# Compound Growth and Decay - Practice Questions","[{\"question\":\"How is compound growth calculated in these GCSE Maths notes?\",\"answer\":\"Compound growth uses a growth formula with the original amount, the percentage rate expressed as a multiplier, and the number of periods to find the amount after n periods.\"},{\"question\":\"What is the difference between compound decay and simple decay?\",\"answer\":\"Compound decay deducts the percentage after each time period, so the reduction compounds over time. Simple decay would not reapply the percentage to the newly reduced value.\"},{\"question\":\"How do compound interest calculations differ from simple interest?\",\"answer\":\"Compound interest applies interest to the balance each period, so the added interest also earns interest later. Simple interest adds a fixed percentage of the original principal each time, which produces a smaller final amount for the same rate and period.\"}]","GCSE Maths - Ratio, Proportion and Rates of Change - Compound Growth and Decay - Notes and Practice Questions | PDF",1788601062,13,{"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":85,"head_meta":87,"extra_data":89,"updated_unix":28},"gcse-maths-ratio-proportion-and-rates-of-change-compound-growth-and-decay-notes-and-practice-questions","",{"@graph":36,"@context":84},[37,53,67],{"@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/gcse-maths-ratio-proportion-and-rates-of-change-compound-growth-and-decay-notes-and-practice-questions/207756/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":61,"encodingFormat":60,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":64,"interactionType":65,"userInteractionCount":4},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"How is compound growth calculated in these GCSE Maths notes?","Question",{"text":74,"@type":75},"Compound growth uses a growth formula with the original amount, the percentage rate expressed as a multiplier, and the number of periods to find the amount after n periods.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"What is the difference between compound decay and simple decay?",{"text":79,"@type":75},"Compound decay deducts the percentage after each time period, so the reduction compounds over time. Simple decay would not reapply the percentage to the newly reduced value.",{"name":81,"@type":72,"acceptedAnswer":82},"How do compound interest calculations differ from simple interest?",{"text":83,"@type":75},"Compound interest applies interest to the balance each period, so the added interest also earns interest later. Simple interest adds a fixed percentage of the original principal each time, which produces a smaller final amount for the same rate and period.","https://schema.org",{"og:url":52,"og:type":86,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":88,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":91},[92,96,100,103,107,112,117,122,127,130,134],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":101,"slug":102},70,"exam",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},"Comic",60,"comic",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},6,"Technology",50,"technology",{"id":113,"doc_module":4,"doc_module_name":46,"category_name":114,"show_sort_weight":115,"slug":116},7,"Healthcare",40,"healthcare",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":119,"show_sort_weight":120,"slug":121},8,"Research & Report",30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"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":21,"slug":137},19,"General","general"]