Discount Factors and Discount Rates

/**
 * Fintech Math Bootcamp · Lesson 014 of 120
 * Discount Factors and Discount Rates
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: One price today for one unit paid later
 * Rule:     DF(t) = (1+r)⁻ᵗ
 *
 * Try it:   What is the discount factor at time zero?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson014() {
  const rate = 0.10;
  const discountFactor = (t: number) => (1 + rate) ** -t;
  const factor = discountFactor(2);
  const result = {factor, present: 1210 * factor};
  return result;
}

export const checkedResult = {"factor":0.8264462809917354,"present":999.9999999999999};

// Run this file directly: npx tsx lessons/02-financial-arithmetic-time-value-and-returns/014-discount-factors-and-discount-rates.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson014(), null, 2));
}

"""
Fintech Math Bootcamp · Lesson 014 of 120
Discount Factors and Discount Rates
Module 02: Financial Arithmetic, Time Value, and Returns

Scenario: One price today for one unit paid later
Rule:     DF(t) = (1+r)⁻ᵗ

Try it:   What is the discount factor at time zero?

Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
Free course:    https://courses.thefintechbuilder.com
Synthetic teaching example, not financial advice or a production library.

Run it: python main.py
"""

import json


def lesson014() -> dict:
    rate = 0.10

    def discount_factor(t: float) -> float:
        return (1 + rate) ** -t

    factor = discount_factor(2)
    result = {"factor": factor, "present": 1210 * factor}
    return result


if __name__ == "__main__":
    print(json.dumps(lesson014(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 014 of 120
 * Discount Factors and Discount Rates
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: One price today for one unit paid later
 * Rule:     DF(t) = (1+r)^(-t)
 *
 * Try it:   What is the discount factor at time zero?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 *
 * Run it: javac Main.java && java Main
 */

import java.util.function.DoubleUnaryOperator;

public class Main {
    static final class DiscountedValue {
        final double factor;
        final double present;

        DiscountedValue(double factor, double present) {
            this.factor = factor;
            this.present = present;
        }
    }

    static DiscountedValue lesson014() {
        double rate = 0.10;
        DoubleUnaryOperator discountFactor = t -> Math.pow(1 + rate, -t);
        double factor = discountFactor.applyAsDouble(2);
        DiscountedValue result = new DiscountedValue(factor, 1210 * factor);
        return result;
    }

    public static void main(String[] args) {
        DiscountedValue result = lesson014();
        System.out.println(object("factor", num(result.factor), "present", num(result.present)));
    }

    // 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 014 of 120
// Discount Factors and Discount Rates
// Module 02: Financial Arithmetic, Time Value, and Returns
//
// Scenario: One price today for one unit paid later
// Rule:     DF(t) = (1+r)⁻ᵗ
//
// Try it:   What is the discount factor at time zero?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
// 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"
	"math"
)

type DiscountedValue struct {
	Factor  float64 `json:"factor"`
	Present float64 `json:"present"`
}

func lesson014() DiscountedValue {
	rate := 0.10
	discountFactor := func(t float64) float64 { return math.Pow(1+rate, -t) }
	factor := discountFactor(2)
	result := DiscountedValue{Factor: factor, Present: 1210 * factor}
	return result
}

func main() {
	printJSON(lesson014())
}

// 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 014 of 120
 * Discount Factors and Discount Rates
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: One price today for one unit paid later
 * Rule:     DF(t) = (1+r)⁻ᵗ
 *
 * Try it:   What is the discount factor at time zero?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
 * 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 DiscountedValue {
    double factor;
    double present;
};

DiscountedValue lesson014() {
    const double rate = 0.10;
    auto discountFactor = [rate](double t) { return std::pow(1 + rate, -t); };
    const double factor = discountFactor(2);
    const DiscountedValue result{factor, 1210 * factor};
    return result;
}

int main() {
    const DiscountedValue result = lesson014();
    std::cout << object({{"factor", num(result.factor)}, {"present", num(result.present)}}) << "\n";
}

//! Fintech Math Bootcamp · Lesson 014 of 120
//! Discount Factors and Discount Rates
//! Module 02: Financial Arithmetic, Time Value, and Returns
//!
//! Scenario: One price today for one unit paid later
//! Rule:     DF(t) = (1+r)⁻ᵗ
//!
//! Try it:   What is the discount factor at time zero?
//!
//! Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
//! Free course:    https://courses.thefintechbuilder.com
//! Synthetic teaching example, not financial advice or a production library.
//!
//! Run it: rustc main.rs && ./main

struct DiscountedValue {
    factor: f64,
    present: f64,
}

fn lesson014() -> DiscountedValue {
    let rate: f64 = 0.10;
    let discount_factor = |t: f64| (1.0 + rate).powf(-t);
    let factor = discount_factor(2.0);
    let result = DiscountedValue { factor, present: 1210.0 * factor };
    result
}

fn main() {
    let result = lesson014();
    println!(
        "{}",
        object(&[("factor", num(result.factor)), ("present", num(result.present))])
    );
}

/// 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 014 of 120
 * Discount Factors and Discount Rates
 * Module 02: Financial Arithmetic, Time Value, and Returns
 *
 * Scenario: One price today for one unit paid later
 * Rule:     DF(t) = (1+r)⁻ᵗ
 *
 * Try it:   What is the discount factor at time zero?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/financial-arithmetic-time-value-and-returns/discount-factors/
 * 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(Lesson014(), jsonOptions));

static DiscountedValue Lesson014()
{
    const double rate = 0.10;
    double DiscountFactor(double t) => Math.Pow(1 + rate, -t);
    var factor = DiscountFactor(2);
    var result = new DiscountedValue(factor, 1210 * factor);
    return result;
}

record DiscountedValue(double Factor, double Present);