Complex mathematical formula in jquery function is not working

Question

EDITED:

The debt ceiling part of the function is actually going to be used in a step that I haven't written yet. It's used to determine if the user's debt to income ratio is too high but it doesn't effect the outcome of the function as it's written now.

I am still having an issue however and would very much appreciate any insight. I think I've got some bad logic in the next section of the javasctipt. Here's my new function:

$(function(){

function calculate_affordability() {

    var income = parseFloat($('#income').val());
    var debts = parseFloat($('#debts').val());
    var apr_decimal = parseFloat($('#apr').val()) / 100;
    var monthly_interest = apr_decimal / 12;
    var down = parseFloat($('#down').val());
    var term = parseFloat($('#term').val()) * 12;

    var debts_ceiling = (debts * .08).toFixed(2);
    var mortgage_ceiling = (income * .28).toFixed(2);

    var formula_numerator = Math.pow((1 + monthly_interest), term) -1;
    var formula_denominator = monthly_interest * Math.pow((1 + monthly_interest), term);
    var formula_result = (formula_numerator / formula_denominator);

    var loan_amount = (mortgage_ceiling * formula_result).toFixed(2);

    //  the issue is in here somewhere:
    var closing_costs = (loan_amount * .03).toFixed(2);
    var actual_down = (down - closing_costs);
    var max_purchase_price = (loan_amount + actual_down);

    $('#monthly-payment').html('$' + mortgage_ceiling);
    $('#loan-amount').html('$' + loan_amount);
    $('#max-purchase-price').html('$' + max_purchase_price);
    $('#actual-down').html('$' + actual_down);
    $('#closing-costs').html('$' + closing_costs);

}


$('#term').keyup(calculate_affordability);

$('#term').mouseup(calculate_affordability);

});

Thanks again for the help!

ORIGINAL:

This is actually a mortgage calculation.

I've got it working when used the normal way - that is, to determine a monthly payment when the user inputs four variables (loan amount, down payment, interest rate, and term years).

But when I try to change the formula to solve for loan amount (an affordability calculator), I'm getting bad results.

Here's the original formula as explained by the Mortgage Professor:

The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005].

P = L[c(1 + c)n]/[(1 + c)n - 1]

http://www.mtgprofessor.com/formulas.htm

I'll first give the example that is working properly.

HTML:

<form>
    <div class="col-md-4">
        <h4>Home Price</h4>
            <input type="text" id="price">
        <h4>Down Payment</h4>
            <input type="text" id="down">
    </div>
    <div class="col-md-4">
        <h4>Rate (%)</h4>
            <input type="text" id="apr">
        <h4>Term (Years)</h4>
            <input type="text" id="term">
    </div>
    <div class="col-md-4">
        Your Monthly Payment:
        <div id="payment"></div>
    </div>
</form>

jQuery:

$(function(){

function calculate_monthly_payment() {

    var price = parseFloat($('#price').val());
    var down = parseFloat($('#down').val());
    var apr_decimal = parseFloat($('#apr').val()) / 100;
    var monthly_interest = apr_decimal / 12;
    var term = parseFloat($('#term').val()) * 12;

    var loan_amount = parseFloat(price - down);

    var formula_numerator = monthly_interest * Math.pow((1 + monthly_interest), term);
    var formula_denominator = Math.pow((1 + monthly_interest), term) -1;

    var monthly_payment = parseFloat(loan_amount * (formula_numerator / formula_denominator)).toFixed(2);

    if (!isNaN(monthly_payment)) {
        $('#payment').html('$' + monthly_payment);
    } else {
        $('#payment').html('Calculating...');
    }

}

$('#price').keyup(calculate_monthly_payment);
$('#down').keyup(calculate_monthly_payment);
$('#apr').keyup(calculate_monthly_payment);
$('#term').keyup(calculate_monthly_payment);

$('#price').mouseup(calculate_monthly_payment);
$('#down').mouseup(calculate_monthly_payment);
$('#apr').mouseup(calculate_monthly_payment);
$('#term').mouseup(calculate_monthly_payment);

});

The part that isn't working properly:

HTML:

<form>
    <div class="col-md-6">
        <h4>Income (Monthly)</h4>
            <input type="text" id="income">
        <h4>Debts (Monthly, not including housing costs)</h4>
            <input type="text" id="debts">
        <h4>Down Payment</h4>
            <input type="text" id="down">
        <h4>Rate (%)</h4>
            <input type="text" id="apr">
        <h4>Term (Years)</h4>
            <input type="text" id="term">
    </div>
    <div class="col-md-6">
        Monthly Payment:
        <div id="monthly-payment"></div>
        Loan Amount:
        <div id="loan-amount"></div>
        Purchase Price:
        <div id="purchase-price"></div>
        Down Payment:
        <div id="actual-down"></div>
        Closing Costs:
        <div id="closing-costs"></div>
    </div>
</form>

jQuery:

$(function(){

function calculate_affordability() {

    var income = parseFloat($('#income').val());
    var debts = parseFloat($('#debts').val());
    var down = parseFloat($('#down').val());
    var apr_decimal = parseFloat($('#apr').val()) / 100;
    var monthly_interest = apr_decimal / 12;
    var term = parseFloat($('#term').val());

    var debt_ceiling = income * .08;
    var monthly_payment = (income * .28).toFixed(2);

    var formula_numerator = monthly_interest * Math.pow((1 + monthly_interest), term);
    var formula_denominator = Math.pow((1 + monthly_interest), term) -1;

    var loan_amount = parseFloat(monthly_payment / (formula_numerator / formula_denominator)).toFixed(2);
    var closing_costs = (loan_amount * .03).toFixed(2);
    var actual_down = (down - closing_costs).toFixed(2);
    var purchase_price = (loan_amount - actual_down).toFixed(2);


    $('#monthly-payment').html('$' + monthly_payment);
    $('#loan-amount').html('$' + loan_amount);
    $('#purchase-price').html('$' + purchase_price);
    $('#actual-down').html('$' + actual_down);
    $('#closing-costs').html('$' + closing_costs);

}


$('#term').keyup(calculate_affordability);

$('#term').mouseup(calculate_affordability);

});

The above is based on looking at the formula and rearranging it.

Original: x = y(a/b)

Solving for y: y = x/(a/b)

Somehow I've gone wrong with the new formula but I'm not sure where nor how to fix it.

Thank you for any help!

Answer 1

Your monthly payment isn't being calculated correctly in the code that isn't working properly. If you look at it, you'll see that you're not factoring in your debts whatsoever.

I'm not sure exactly how you're choosing to calculate the monthly payment, but my guess is you need to subtract your debts from your income and then do your ceiling math, maybe something like this:

var debt_ceiling = (income - debts) * .92;
var monthly_payment = (debt_ceiling * .28).toFixed(2);

Or something like that... but in there is your error, I think.

Answer 2

Semi-Solved:

The issue was with my formula and a colleague and I figured out the major problem. When I converted the original formula (which I didn't outline in very good detail here), I didn't perform the proper algebraic method of reversing what was done to one side of the equation on the other side. Basically, the fraction bit of the original formula needed to be flipped and multiplied. So here's the new formula, solving for L rather than P:

L = P[(1 + c)^n -1]/[c(1 + c)^n]

And the original with the carrots to signify "raised to the power of n": P = L[c(1 + c)^n]/[(1 + c)^n - 1]

Still having an issue though, which I added to my original question.

Answer 3

the new formula become L= P / [(1+c)^n-1]/[c(1+c)^n]

let me work this out for you. To add L to the other side you have to multiple by 1/L. so now the left side of the equation is P/L. to get rid of the P you have to multiple 1/P. now leaving the L alone makes the L into a ratio of 1/L. To get rid of the one you have to reverse the equationon the right side. so you get the new formula above.