loan-calculator-apr-scripting-rule.js

/* -- APR Calculator Scripting rule -- */

// --------------------
// STEP 1: Initialize variables

// 1.1: Define and assign the loan variables using the input object.
const loanAmount = input.loanAmount;
const monthlyPayment = input.monthlyPayment;
const loanDuration = input.loanDuration;

// 1.2: Define the APR variable, but do not assign a value to it yet.
let apr; 
// --------------------

// --------------------
// STEP 2: Define two functions: calculateF(x) and calculateFDerivative(x). These functions are used in Newton's method algorithm to find the value of x that makes f(x) = 0, where f(x) is defined as the sum of the loan amount divided by the monthly payment minus the sum of x to the power of i (where i ranges from 1 to loanDuration).

// 2.1: Declare a function that calculates the value of f(x).
function calculateF(x) {
    let sumOfPowers = 0;
    for (let i = 1; i <= loanDuration; i++) {
        sumOfPowers += Math.pow(x, i);
    }
    return sumOfPowers - loanAmount / monthlyPayment;
}

// 2.2: Declare a function that calculates the derivative of f(x).
function calculateFDerivative(x) {
    let sumOfPowerTimesIndex = 0;
    for (let i = 1; i <= loanDuration; i++) {
        sumOfPowerTimesIndex += i * Math.pow(x, i - 1);
    }
    return sumOfPowerTimesIndex;
}
// --------------------

// --------------------
// STEP 3: Define the variables required to solve the APR and use Newton's method algorithm.

// 3.1: Define a variable to solve the APR. It starts with an initial guess of 1.
let x = 1;

// 3.2: Define the level of precision that we aim for in the solution. In our case, we use the value of Epsilon.
const EPSILON = 1e-6;

// 3.3: Define the amount that we use to adjust the value of x on each iteration of Newton's method algorithm.
let delta = 0;

// 3.4: Use Newton's method algorithm to iteratively adjust the value of x until f(x) = 0 with a level of precision specified by the EPSILON constant.
do {
    // 3.4.1: Calculate the change in x that is needed to make f(x) = 0.
    delta = -calculateF(x) / calculateFDerivative(x);
    // 3.4.2: Update the value of x
    x += delta;
} while (Math.abs(delta) > EPSILON);
// --------------------

// --------------------
// STEP 4: Calculate the APR value, round it to 2 decimal places, and set the rounded value as an output.

// 4.1: Calculate the APR using the following formula:
apr = Math.pow(x, -12) - 1;

// 4.2: Round the calculated APR value to 2 decimal places.
let aprRounded = parseFloat((apr * 100).toFixed(2));

// 4.3: Set the rounded value as an output.
output.apr = aprRounded;

// 4.4: Return the output.
return output
// --------------------