Percentage Change, Percentage Points, and Basis Points

/**
 * Fintech Math Bootcamp · Lesson 004 of 120
 * Percentage Change, Percentage Points, and Basis Points
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A loan-rate change reported three different ways
 * Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
 *
 * Try it:   What is a change from 3% to 3.5% in basis points?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson004() {
  const before = 0.08, after = 0.09;
  const delta = after - before;
  const result = {
    points: delta * 100,
    basisPoints: delta * 10000,
    relative: delta / before
  };
  return result;
}

export const checkedResult = {"points":0.9999999999999996,"basisPoints":99.99999999999994,"relative":0.12499999999999993};

// Run this file directly: npx tsx lessons/01-mathematical-language-and-quantitative-reasoning/004-percentage-change-percentage-points-and-basis-points.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson004(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 004 of 120
Percentage Change, Percentage Points, and Basis Points
Module 01: Mathematical Language and Quantitative Reasoning

Scenario: A loan-rate change reported three different ways
Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative

Try it:   What is a change from 3% to 3.5% in basis points?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json


def lesson004() -> dict:
    before, after = 0.08, 0.09
    delta = after - before
    result = {
        "points": delta * 100,
        "basisPoints": delta * 10000,
        "relative": delta / before,
    }
    return result


if __name__ == "__main__":
    print(json.dumps(lesson004(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 004 of 120
 * Percentage Change, Percentage Points, and Basis Points
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A loan-rate change reported three different ways
 * Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
 *
 * Try it:   What is a change from 3% to 3.5% in basis points?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

public class Main {
    static final class RateChange {
        final double points;
        final double basisPoints;
        final double relative;

        RateChange(double points, double basisPoints, double relative) {
            this.points = points;
            this.basisPoints = basisPoints;
            this.relative = relative;
        }
    }

    static RateChange lesson004() {
        double before = 0.08, after = 0.09;
        double delta = after - before;
        RateChange result = new RateChange(
            delta * 100,
            delta * 10000,
            delta / before
        );
        return result;
    }

    public static void main(String[] args) {
        RateChange result = lesson004();
        System.out.println(object(
            "points", num(result.points),
            "basisPoints", num(result.basisPoints),
            "relative", num(result.relative)));
    }

    // Formats a double the way JSON.stringify does: whole numbers without ".0", null for NaN or infinity.
    static String num(double x) {
        if (Double.isNaN(x) || Double.isInfinite(x)) return "null";
        if (x == Math.rint(x) && Math.abs(x) < 1e15) return String.valueOf((long) x);
        return String.valueOf(x);
    }

    static String quote(String text) {
        return "\"" + text.replace("\\", "\\\\").replace("\"", "\\\"") + "\"";
    }

    // Indents an already formatted JSON value by one level.
    static String nested(String json) {
        return json.replace("\n", "\n  ");
    }

    static String object(String... keysAndValues) {
        if (keysAndValues.length == 0) return "{}";
        StringBuilder out = new StringBuilder("{");
        for (int i = 0; i < keysAndValues.length; i += 2) {
            out.append(i == 0 ? "\n  " : ",\n  ")
               .append(quote(keysAndValues[i])).append(": ").append(nested(keysAndValues[i + 1]));
        }
        return out.append("\n}").toString();
    }
}

// Fintech Math Bootcamp · Lesson 004 of 120
// Percentage Change, Percentage Points, and Basis Points
// Module 01: Mathematical Language and Quantitative Reasoning
//
// Scenario: A loan-rate change reported three different ways
// Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
//
// Try it:   What is a change from 3% to 3.5% in basis points?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.
//
// Run it: go run main.go

package main

import (
	"encoding/json"
	"fmt"
)

type RateChange struct {
	Points      float64 `json:"points"`
	BasisPoints float64 `json:"basisPoints"`
	Relative    float64 `json:"relative"`
}

func lesson004() RateChange {
	before, after := 0.08, 0.09
	delta := after - before
	result := RateChange{
		Points:      delta * 100,
		BasisPoints: delta * 10000,
		Relative:    delta / before,
	}
	return result
}

func main() {
	printJSON(lesson004())
}

// printJSON prints a value as JSON indented with two spaces, like JSON.stringify(value, null, 2).
func printJSON(value any) {
	out, err := json.MarshalIndent(value, "", "  ")
	if err != nil {
		panic(err)
	}
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 004 of 120
 * Percentage Change, Percentage Points, and Basis Points
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A loan-rate change reported three different ways
 * Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
 *
 * Try it:   What is a change from 3% to 3.5% in basis points?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: g++ -std=c++17 -o main main.cpp && ./main
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// Formats a double the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
std::string num(double x) {
    if (!std::isfinite(x)) return "null";
    char buffer[32];
    auto [end, error] = std::to_chars(buffer, buffer + sizeof buffer, x);
    (void)error;
    return std::string(buffer, end);
}

std::string quote(const std::string& text) {
    std::string out = "\"";
    for (char c : text) {
        if (c == '"' || c == '\\') out += '\\';
        out += c;
    }
    return out + "\"";
}

// Indents an already formatted JSON value by one level.
std::string nested(const std::string& json) {
    std::string out;
    for (char c : json) {
        out += c;
        if (c == '\n') out += "  ";
    }
    return out;
}

std::string object(const std::vector<std::pair<std::string, std::string>>& fields) {
    if (fields.empty()) return "{}";
    std::string out = "{";
    for (std::size_t i = 0; i < fields.size(); ++i) {
        out += i == 0 ? "\n  " : ",\n  ";
        out += quote(fields[i].first) + ": " + nested(fields[i].second);
    }
    return out + "\n}";
}

struct RateChange {
    double points;
    double basisPoints;
    double relative;
};

RateChange lesson004() {
    const double before = 0.08, after = 0.09;
    const double delta = after - before;
    const RateChange result{
        delta * 100,
        delta * 10000,
        delta / before
    };
    return result;
}

int main() {
    const RateChange result = lesson004();
    std::cout << object({
        {"points", num(result.points)},
        {"basisPoints", num(result.basisPoints)},
        {"relative", num(result.relative)}
    }) << "\n";
}

//! Fintech Math Bootcamp · Lesson 004 of 120
//! Percentage Change, Percentage Points, and Basis Points
//! Module 01: Mathematical Language and Quantitative Reasoning
//!
//! Scenario: A loan-rate change reported three different ways
//! Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
//!
//! Try it:   What is a change from 3% to 3.5% in basis points?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct RateChange {
    points: f64,
    basis_points: f64,
    relative: f64,
}

fn lesson004() -> RateChange {
    let (before, after) = (0.08, 0.09);
    let delta = after - before;
    let result = RateChange {
        points: delta * 100.0,
        basis_points: delta * 10000.0,
        relative: delta / before,
    };
    result
}

fn main() {
    let result = lesson004();
    println!(
        "{}",
        object(&[
            ("points", num(result.points)),
            ("basisPoints", num(result.basis_points)),
            ("relative", num(result.relative)),
        ])
    );
}

/// Formats a number the way JSON.stringify does: shortest round-trip form, null for NaN or infinity.
fn num(x: f64) -> String {
    if x.is_finite() {
        format!("{}", x)
    } else {
        "null".to_string()
    }
}

fn quote(text: &str) -> String {
    format!("\"{}\"", text.replace('\\', "\\\\").replace('"', "\\\""))
}

/// Indents an already formatted JSON value by one level.
fn nested(json: &str) -> String {
    json.replace('\n', "\n  ")
}

fn object(fields: &[(&str, String)]) -> String {
    if fields.is_empty() {
        return "{}".to_string();
    }
    let lines: Vec<String> = fields
        .iter()
        .map(|(key, value)| format!("  {}: {}", quote(key), nested(value)))
        .collect();
    format!("{{\n{}\n}}", lines.join(",\n"))
}

/**
 * Fintech Math Bootcamp · Lesson 004 of 120
 * Percentage Change, Percentage Points, and Basis Points
 * Module 01: Mathematical Language and Quantitative Reasoning
 *
 * Scenario: A loan-rate change reported three different ways
 * Rule:     8% → 9% = +1 pp = +100 bp = +12.5% relative
 *
 * Try it:   What is a change from 3% to 3.5% in basis points?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/mathematical-language-and-quantitative-reasoning/percentage-change-percentage-points-and-basis-points/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: dotnet run  (inside a console project that holds this Program.cs)
 */

using System.Text.Json;

var jsonOptions = new JsonSerializerOptions { WriteIndented = true, PropertyNamingPolicy = JsonNamingPolicy.CamelCase };
Console.WriteLine(JsonSerializer.Serialize(Lesson004(), jsonOptions));

static RateChange Lesson004()
{
    double before = 0.08, after = 0.09;
    var delta = after - before;
    var result = new RateChange(
        Points: delta * 100,
        BasisPoints: delta * 10000,
        Relative: delta / before
    );
    return result;
}

record RateChange(double Points, double BasisPoints, double Relative);