Amortize.js

1. About this program info
2. Source Code code
- 2.1. Calculate Payment
- 2.2. Calculate Schedule
3. Tests code

1 About this program info

This is a literate program authored in org-mode.

The program generate a JavaScript file called amortize.js.

2 Source Code code

The source code is written JavaScript; and implements:

function name	purpose
pmt	Calculate amortized payment
compute-schedule	Computes amortization schedule as multi-dimensional array

2.1 Calculate Payment

The function 'pmt' computes the payment amount for a loan.

The function accepts arguments:

name	comments
rate	is the interest rate for the loan.
nper	is the total number of payments for the loan.
pv	is the present value, or the total amount that a series of future payments is worth now; also known as the principal.

The function signature:
```
pmt(rate,nper,pv)
```
In order to calculate the payment we need to first calculate the Present Value Interest Factor (PVIF).o
```
pvif = Math.pow( 1 + rate, nper);
```
Using the PVIF we can calculate the payment.
```
pmt = rate / (pvif - 1) * -(pv * pvif);
```

Finally, the sections are combined into a function.

function pmt(rate,nper,pv) {
    var pvif, pmt;

    pvif = Math.pow( 1 + rate, nper);
    pmt = rate / (pvif - 1) * -(pv * pvif);   

    return pmt;
};

2.2 Calculate Schedule

The 'computeSchedule' function to compute amortization schedule is named 'computeSchedule'.

The function accepts arguments:

name	comments
loan_amount	is the amount borrowed to purchase the property.
interest_rate	is the percentage used to calculate interest due.
payments_per_year	is the number of payments made in a calendar year.
years	is the number of years.
payment	is the amount of the payment each period.

The function signature is:

computeSchedule(loan_amount, interest_rate, payments_per_year, years, payment)

Define an array to capture the schedule.
```
var schedule = [];
```
Define a variable to track the remaining balance.
```
var remaining = loan_amount;
```

Compute the total number of payments.

var number_of_payments = payments_per_year * years;

Loop through all of the periods and capture the entries in the schedule.

for (var i=0; i<=number_of_payments; i++) {
    var interest = remaining * (interest_rate/100/payments_per_year);
    var principle = (payment-interest);
    var row = [i, principle>0?principle:0, interest>0?interest:0, remaining>0?remaining:0];
    schedule.push(row);
    remaining -= principle
}

Finally, the sections are combined into a function.

function computeSchedule(loan_amount, interest_rate, payments_per_year, years, payment) {
    var schedule = [];
    var remaining = loan_amount;
    var number_of_payments = payments_per_year * years;

    for (var i=0; i<=number_of_payments; i++) {
        var interest = remaining * (interest_rate/100/payments_per_year);
        var principle = (payment-interest);
        var row = [i, principle>0?principle:0, interest>0?interest:0, remaining>0?remaining:0];
        schedule.push(row);
        remaining -= principle
    }

    return schedule;
}

3 Tests code

3.1 Should be 297.47

function pmt(rate,nper,pv) {
    var pvif, pmt;

    pvif = Math.pow( 1 + rate, nper);
    pmt = rate / (pvif - 1) * -(pv * pvif);   

    return pmt;
};

console.log('loan_amount: ' + loan_amount);
console.log('interest_rate: ' + interest_rate);
console.log('payments_per_year: ' + payments_per_year);
console.log('years: ' + years);
console.log( "The calculated payment is: " + 
             pmt(interest_rate/100/payments_per_year, payments_per_year * years, -loan_amount)
             .toFixed(2) );

loan_amount: 10000
interest_rate: 4.5
payments_per_year: 12
years: 3
The calculated payment is: 297.47

3.2 Should be 2245.22

loan_amount: 500000
interest_rate: 3.5
payments_per_year: 12
years: 30
The calculated payment is: 2245.22

3.3 Generate Schedule

function computeSchedule(loan_amount, interest_rate, payments_per_year, years, payment) {
    var schedule = [];
    var remaining = loan_amount;
    var number_of_payments = payments_per_year * years;

    for (var i=0; i<=number_of_payments; i++) {
        var interest = remaining * (interest_rate/100/payments_per_year);
        var principle = (payment-interest);
        var row = [i, principle>0?principle:0, interest>0?interest:0, remaining>0?remaining:0];
        schedule.push(row);
        remaining -= principle
    }

    return schedule;
}

console.log('loan_amount: ' + loan_amount);
console.log('interest_rate: ' + interest_rate);
console.log('payments_per_year: ' + payments_per_year);
console.log('years: ' + years);
console.log('payment: ' + payment);
console.log( JSON.stringify(
    computeSchedule(loan_amount, interest_rate, payments_per_year, years, payment), 0, 4
))

loan_amount: 10000
interest_rate: 4.5
payments_per_year: 12
years: 3
payment: 297.47
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