28:null 29:["$","title",null,{"children":"Compound interest | Martien van Steenbergen | Observable"}] 2e:T5cd,compoundInterestPlot = (domain, factors, yearsForFactor, lineLabelPoints) => { const percentage = d => d.interest + "%"; return Plot.plot({ title: "Compound interest’s exponential growth curves", subtitle: "acts like cancer in our social structure, hence self-destructs if untreated", grid: true, legend: true, // clip: true, x: { domain: domain.x, }, y: { domain: domain.y, ticks: 5, }, marks: [ Plot.line( factors, { x: "year", y: "factor", stroke: "interest", } ), Plot.dot( yearsForFactor, { x: "year", y: "factor", r: 3, fill: "red" } ), Plot.dot( lineLabelPoints, { x: "year", y: "factor", z: "interest", fill: "white", r: 9 } ), Plot.text( lineLabelPoints, { x: "year", y: "factor", z: "interest", text: percentage, fontWeight: "bold", } ), Plot.tip( factors, Plot.pointerX({x: "year", y: "factor"}) ), ], // make plot size multiples of 36 // make margins 1 x 36 // therefore: frame = 16*36 x 10*36: resulting in a square grid width: 18*36, height: 12*36, marginTop: 36, marginBottom: 36, marginLeft: 36, marginRight: 36, }) }2f:[] 2c:{"id":"f6567d2b52a98484","slug":"compound-interest","title":"Compound interest","thumbnail":"43d5dc4771c74d9f84127f0bd4ddfa39c51a66ceb705db9392311fd81d4c6c36","access_level":"public","create_time":"$D2024-07-03T14:25:23.993Z","update_time":"$D2024-07-10T13:31:00.245Z","view_time":null,"first_public_time":"$D2024-07-03T14:27:04.589Z","has_unpublished_edits":null,"fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"6e89ba4444f0cc85","login":"martien","name":"Martien van Steenbergen","avatar_url":"https://avatars-next.observableusercontent.com/40dc8e4f86d0cf89184b173b4d1d88336e5728c175479f33261ced3496adb3c2","tier":"starter_2024"},"version":64,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"3c5ecb707ecd20a7","login":"martien","name":"Martien van Steenbergen","avatar_url":"https://avatars-next.observableusercontent.com/40dc8e4f86d0cf89184b173b4d1d88336e5728c175479f33261ced3496adb3c2","tier":null}],"members":[{"type":"individual","id":"3c5ecb707ecd20a7","login":"martien","name":"Martien van Steenbergen","avatar_url":"https://avatars-next.observableusercontent.com/40dc8e4f86d0cf89184b173b4d1d88336e5728c175479f33261ced3496adb3c2","tier":null,"role":"editor"},{"type":"team","id":"6e89ba4444f0cc85","login":"martien","name":"Martien van Steenbergen","avatar_url":"https://avatars-next.observableusercontent.com/40dc8e4f86d0cf89184b173b4d1d88336e5728c175479f33261ced3496adb3c2","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":1,"collection":null,"type":"notebook","body":{"title":"Compound interest","cells":[{"id":6,"value":"# Compound interest","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":55,"value":"**[Compound interest](https://en.wikipedia.org/wiki/Compound_interest)** is interest accumulated from a [principal](https://en.wikipedia.org/wiki/Debt#Principal) _**plus**_ previously accumulated interest.\nTherefore, it follows an [exponential growth](https://en.wikipedia.org/wiki/Exponential_growth) pattern.\nAs such, it doubles, triples, quadruples or _n_-folds the principal at certain points. For example, with 2% compound interest, the principle is doubled in year 35.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":7,"value":"compoundInterestPlot(domain, factors, yearsForFactor, lineLabelPoints)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":53,"value":"viewof factor = Inputs.range([2,25], {label: \"Growth Factor\", value: 2, step: 1})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"Examples can be found in financial loans and mortgages, pyramid schemes, internet memes, bacterial growth, virus spreading, cancer growth, avalanche breakdown, nuclear chain reactions, positive feedback resulting in growth of an amplified audio signal.\n\nIn the biological realm, this growth pattern can occur where there is sickness or death.\nCancer, for instance, follows an exponential growth pattern.\nIt grows slowly first, although constantly accelerating.\nOften by the time it has been discovered it has entered a growth phase where it cannot be stopped.\n\nExponential growth in the biological realm usually ends with the death of the host organism and/or the environment on which it depends.\nIn that sense, **compound interest acts like cancer in our social structure, hence self-destructs** if untreated.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":10,"value":"interests = [1, 2, 3, 5, 6, 8, 12] // number of interest lines plotted","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"length = 75 // number of years to show (Plot.x.domain)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"domain = ({\n x: [0, length],\n y: [0, 25],\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"A `Factor` is a location in the plot, where `year` is the `x`, and `factor` is the `y`.\n```ts\ntype Factor = {\n year: number; // year number [0, length>\n interest: number; // interest value in percent\n factor: number; // growth factor in given year with given interest\n}\n```","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":49,"value":"\n \n \n \n \n \n \n\n

do	in order to
\n precook data needed in separate cells, to be used (‘imported’) by the Plot(),\n rather than deriving or filtering values on the fly\n	\n \n keep the plot as straightforward as possible \n make all data easy to inspect, hence debug \n \n

\n\n|in order to|create|containing\n|---|---|\n|draw the lines|[factors](#factors)|a Factor[], with a factor for each year and each interest|\n|label each line with its interest|[lineLabelPoints](#lineLabelPoints)|a Factor[] for each of the lines, just inside the frame|\n|show a dot for a given growth factor on each line|[yearsForFactor](#yearsForFactor)|a Factor[] for the dots|","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":13,"value":"// Factor[] for all years and all interests\nviewof factors = tabler(factorForYear(domain.x[1]))(interests)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":47,"value":"// Factor[] for interest line labels\nviewof lineLabelPoints = \n{\n // move inward from frame; values are in user space\n const xMax = domain.x[1] - 3;\n const yMax = domain.y[1] - 2;\n const x = yearsToReachFactor(yMax);\n const y = futureValue(xMax);\n return Inputs.table(\n interests.map(\n interest => ({\n interest,\n factor: Math.min(yMax, y(interest)),\n year: Math.min(xMax, x(interest)),\n })\n ),\n tableFormat\n )\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":15,"value":"// Factor[] for all interests where factor === growthFactor\nviewof yearsForFactor = tabler\n(yearForFactor(factor)(yearsToReachFactor(factor)))\n(interests)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"// takes factor, returns function that\n// takes yearFactor, returns function that\n// takes interest\n// returns corresponding Factor with corresponding year\nyearForFactor =\n(factor) =>\n(yearFactor) =>\n(interest) =>\n({\n factor,\n interest,\n year: yearFactor(interest),\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":44,"value":"yearForFactor(3)(yearsToReachFactor(3))(2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":43,"value":"yearsToReachFactor(3)(2)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"$2e","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":18,"value":"// takes number of years interest accrues, returns function that\n// takes interest percentage\n// returns Factor[] for each of the years\nfactorForYear =\n(length) =>\n(interest) =>\nArray.from(\n {length},\n (_, year) => futureFactor(year)(interest)\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":19,"value":"// take interest percentage, returns function that\n// takes year\n// returns Factor for given interest and year\nfutureFactor =\n(year) =>\n(interest) =>\n({\n year,\n interest,\n factor: futureValue(year)(interest)\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"futureValue =\n(year) =>\n(interest) =>\nMath.pow(1 + interest / 100, year)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"futureFactor(35)(2) // 2% interests leads to double the principle in 35 years","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"// takes factor, returns function that\n// takes interest\n// returns year in which interest leads to exactly factor\n// e.g. yearsToReachFactor(2)(3) → 35\nyearsToReachFactor =\n(factor) =>\n(interest) =>\nMath.log(factor) / Math.log(1 + interest / 100)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":22,"value":"// 2% interests leads to double the principle in 35 years\n// given a 2% compound interest rate,\n// in which year is the Future Value twice the Present Value\nyearsToReachFactor\n (2) // doubled\n (2) // interest rate in percent\n// → ~35","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"tabler = table(tableFormat)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":34,"value":"tableFormat = {\n const ƒ = (d) => d.toFixed(2);\n return ({width: 320, format: {year: ƒ, factor: ƒ}});\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"table =\n(format) =>\n(ƒ) =>\n(list) =>\nInputs.table(list.flatMap(ƒ), format)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W2f","stdlib":"1","titling":"auto"}} 2d:"$2c:body"