Math.log instead of recursive method - flaw in my formula

Question

I just got solved this problem: Conversion from VBA to JS - wrong output (thanks to Terry Lennox!)

But I'd rather would like to do the same calculation with Math.log in stead of the recursive method, my customer suggested.

I am having the following code:

var amount = parseFloat($('#input_loan_amount').val()); //value: 250000
var initial_fee = parseFloat($('#input_initial_fee').val()); //value: 3499
var monthly_fee = parseFloat($('#input_monthly_fee').val()); //value: 99
var monthly = parseFloat($('#input_monthly_interest').val()); //value: 0.41
var rate = parseFloat($('#input_installment').val()); //value:3499
$('#result_albert').html('Calculating ...');

if (amount > 0) {
  amount = amount + initial_fee;
  if (isNaN(monthly) == true) {
    monthly = 0;
  }
  if (isNaN(rate) == true) {
    rate = 0;
  }

  monthly = monthly / 100;
  var monthly2 = Math.round(monthly * 100) / 100;
  var months = -(Math.log(1 - (monthly * amount / (rate - monthly_fee)))) / Math.log(1 + monthly);

  months = -(Math.log(Math.round((1 - (monthly * amount / (rate - monthly_fee))) * 100) / 100) / Math.log(Math.round((1 + monthly) * 100) / 100));
}

The number before the dot is correct, but the decimals are not correct. I reckon, my formula months= is not quite correct, but my mathematic skills are not high enough ...

user_7237224 · Answer

We can use the formula explained here: https://math.stackexchange.com/questions/3185889/how-do-i-solve-for-n-number-of-periods-in-a-loan-repayment-formula

To get us the number of months required or duration, this is basically what the NPER formula will give us in Excel.

// Using the formula n = log(A/(A-rP))
// A: monthly payment
// P: principal
// r: rate
function nper(A, P, r) { 
    return Math.log(A/(A-r*P))/Math.log1p(r);
} 

function calculate() {
    var amount = parseFloat($('#input_loan_amount').val()); //value: 250000
    var initial_fee = parseFloat($('#input_initial_fee').val()); //value: 3499
    var monthly_fee = parseFloat($('#input_monthly_fee').val()); //value: 99
    var monthly = parseFloat($('#input_monthly_interest').val()); //value: 0.41
    var rate = parseFloat($('#input_installment').val()); //value:3499
    
    amount=amount+initial_fee;
    monthly_payment = rate - monthly_fee;
    monthly=monthly/100;
                        
    // Using formula from https://math.stackexchange.com/questions/3185889/how-do-i-solve-for-n-number-of-periods-in-a-loan-repayment-formula
    const durationMonths = nper(monthly_payment, amount, monthly);

    const roundedDuration = Math.ceil(durationMonths);
    const runningAdm = roundedDuration * monthly_fee;

    $('#durationOutput').html(roundedDuration);
    $('#runningAdm').html(runningAdm);

}

calculate()




 Loan amount:
 
 


 Initial fee:
 
 

 
 Monthly fee:
 
 

 
  Monthly interest (%):
 
 

 
 Fixed price:
 
 

 
 

 Duration (months): 

 Running Adm.:

Math.log instead of recursive method - flaw in my formula

1 Answers