A "Mortgage" (historically a "death pledge") represents a significant long-term commitment of resources. This estimator moves away from standard financial terminology to look at the pure mathematical logic of asset acquisition. By inputting the Total Asset Volume and subtracting your Initial Equity Offset, you establish the Net Obligation.
The Annual Expansion Factor represents the compounding growth applied to the obligation over time. Unlike a simple flat fee, this factor compounds periodically, meaning the duration of the Temporal Cycle heavily influences the total resources required to satisfy the pledge.
Mathematical Formula Used
The calculation utilizes the standard amortization formula to determine the periodic flow of units required to neutralize the obligation:
P = [ r * PV ] / [ 1 – (1 + r)^-n ]
PV: Net Obligation (Asset Volume – Initial Offset)
Imagine a project requiring 400,000 units of material. You provide 80,000 units immediately (Initial Offset), leaving 320,000 as the Net Obligation. Over a 20-year Temporal Cycle with a 4% Expansion Factor, the math reveals a monthly requirement of approximately 1,939 units, with an Aggregate Lifetime Commitment of 465,360 units by the end of the cycle.
function calculateCommitment() {
var assetVolume = parseFloat(document.getElementById("assetVolume").value);
var initialOffset = parseFloat(document.getElementById("initialOffset").value);
var expansionFactor = parseFloat(document.getElementById("expansionFactor").value);
var temporalCycle = parseFloat(document.getElementById("temporalCycle").value);
if (isNaN(assetVolume) || isNaN(initialOffset) || isNaN(expansionFactor) || isNaN(temporalCycle) || assetVolume <= initialOffset) {
alert("Please enter valid positive numbers. Ensure Total Asset Volume is greater than the Initial Offset.");
return;
}
var principal = assetVolume – initialOffset;
var monthlyRate = (expansionFactor / 100) / 12;
var totalPeriods = temporalCycle * 12;
var periodicVal;
if (monthlyRate === 0) {
periodicVal = principal / totalPeriods;
} else {
periodicVal = principal * (monthlyRate * Math.pow(1 + monthlyRate, totalPeriods)) / (Math.pow(1 + monthlyRate, totalPeriods) – 1);
}
var aggregateVal = periodicVal * totalPeriods;
var expansionAccrual = aggregateVal – principal;
document.getElementById("netObligation").innerText = principal.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("periodicRequirement").innerText = periodicVal.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("aggregateCommitment").innerText = aggregateVal.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("totalExpansion").innerText = expansionAccrual.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("resultDisplay").style.display = "block";
}