/* Calculator Container Styling */
.ndr-calculator-wrapper {
font-family: 'Segoe UI', Roboto, Helvetica, Arial, sans-serif;
max-width: 800px;
margin: 0 auto;
padding: 20px;
background-color: #f9fbfd;
border: 1px solid #e1e4e8;
border-radius: 8px;
box-shadow: 0 4px 12px rgba(0,0,0,0.05);
}
.ndr-calc-header {
text-align: center;
margin-bottom: 25px;
border-bottom: 2px solid #0056b3;
padding-bottom: 15px;
}
.ndr-calc-header h2 {
color: #0056b3;
margin: 0;
font-size: 24px;
}
.ndr-input-group {
margin-bottom: 20px;
background: #fff;
padding: 15px;
border-radius: 6px;
border: 1px solid #eee;
}
.ndr-label {
display: block;
font-weight: 600;
margin-bottom: 8px;
color: #333;
}
.ndr-input-wrapper {
position: relative;
display: flex;
align-items: center;
}
.ndr-input {
width: 100%;
padding: 12px;
font-size: 16px;
border: 1px solid #ccc;
border-radius: 4px;
transition: border-color 0.3s;
}
.ndr-input:focus {
border-color: #0056b3;
outline: none;
}
.ndr-suffix {
position: absolute;
right: 15px;
color: #666;
font-weight: 500;
}
.ndr-btn {
width: 100%;
background-color: #0056b3;
color: white;
padding: 14px;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
.ndr-btn:hover {
background-color: #004494;
}
.ndr-result-box {
margin-top: 25px;
background-color: #e8f4fd;
border: 1px solid #b6dbf9;
border-radius: 6px;
padding: 20px;
display: none; /* Hidden by default */
text-align: center;
}
.ndr-result-value {
font-size: 32px;
font-weight: 800;
color: #0056b3;
margin: 10px 0;
}
.ndr-result-label {
font-size: 14px;
color: #555;
text-transform: uppercase;
letter-spacing: 1px;
}
.ndr-secondary-result {
margin-top: 10px;
font-size: 14px;
color: #444;
border-top: 1px solid #b6dbf9;
padding-top: 10px;
}
/* Tabs for different calculation methods */
.ndr-tabs {
display: flex;
margin-bottom: 20px;
border-bottom: 1px solid #ccc;
}
.ndr-tab {
padding: 10px 20px;
cursor: pointer;
background: #f1f1f1;
border: 1px solid #ccc;
border-bottom: none;
margin-right: 5px;
border-radius: 4px 4px 0 0;
}
.ndr-tab.active {
background: #fff;
border-bottom: 2px solid #fff;
font-weight: bold;
color: #0056b3;
margin-bottom: -1px;
}
.ndr-tab-content {
display: none;
}
.ndr-tab-content.active {
display: block;
}
/* Content Styling */
.ndr-article {
margin-top: 50px;
font-family: 'Segoe UI', Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
}
.ndr-article h2 { color: #0056b3; margin-top: 30px; }
.ndr-article h3 { color: #444; margin-top: 20px; }
.ndr-article p { margin-bottom: 15px; }
.ndr-article ul { margin-bottom: 20px; padding-left: 20px; }
.ndr-article li { margin-bottom: 8px; }
.ndr-formula-box {
background: #f4f4f4;
padding: 15px;
border-left: 4px solid #0056b3;
font-family: monospace;
margin: 20px 0;
}
// Tab Switching Logic
function switchTab(method) {
// Hide all contents
document.getElementById('content-fisher').classList.remove('active');
document.getElementById('content-cashflow').classList.remove('active');
document.getElementById('tab-fisher').classList.remove('active');
document.getElementById('tab-cashflow').classList.remove('active');
document.getElementById('resultBox').style.display = 'none';
// Show selected
document.getElementById('content-' + method).classList.add('active');
document.getElementById('tab-' + method).classList.add('active');
}
// Method 1: Fisher Equation Calculation
function calculateFisher() {
// Get Inputs
var r_real = parseFloat(document.getElementById('realRate').value);
var i_inflation = parseFloat(document.getElementById('inflationRate').value);
var resultBox = document.getElementById('resultBox');
var resultDisplay = document.getElementById('finalResult');
var secondaryDisplay = document.getElementById('secondaryInfo');
// Validation
if (isNaN(r_real) || isNaN(i_inflation)) {
alert("Please enter valid numbers for both Real Rate and Inflation Rate.");
return;
}
// Calculation: (1 + r)(1 + i) – 1
var dec_real = r_real / 100;
var dec_inflation = i_inflation / 100;
var nominal_decimal = ((1 + dec_real) * (1 + dec_inflation)) – 1;
var nominal_percent = nominal_decimal * 100;
// Approximation (r + i)
var approx_percent = r_real + i_inflation;
// Display
resultBox.style.display = 'block';
resultDisplay.innerHTML = nominal_percent.toFixed(4) + "%";
secondaryDisplay.innerHTML = "Linear Approximation (Real + Inflation): " + approx_percent.toFixed(4) + "%Difference due to compounding: " + (nominal_percent – approx_percent).toFixed(4) + "%";
}
// Method 2: Cash Flow Calculation
function calculateCashFlowRate() {
// Get Inputs
var pv = parseFloat(document.getElementById('presentValue').value);
var fv = parseFloat(document.getElementById('futureValue').value);
var t = parseFloat(document.getElementById('timePeriod').value);
var resultBox = document.getElementById('resultBox');
var resultDisplay = document.getElementById('finalResult');
var secondaryDisplay = document.getElementById('secondaryInfo');
// Validation
if (isNaN(pv) || isNaN(fv) || isNaN(t) || t <= 0 || pv === 0) {
alert("Please enter valid non-zero values. Time period must be greater than 0.");
return;
}
// Calculation: (FV / PV)^(1/t) – 1
var rate_decimal = Math.pow((fv / pv), (1 / t)) – 1;
var rate_percent = rate_decimal * 100;
// Display
resultBox.style.display = 'block';
resultDisplay.innerHTML = rate_percent.toFixed(4) + "%";
secondaryDisplay.innerHTML = "This is the nominal annual compounded growth rate (CAGR) required to turn " + pv + " into " + fv + " over " + t + " years.";
}
What is a Nominal Discount Rate?
The Nominal Discount Rate is the interest rate used in Discounted Cash Flow (DCF) analysis that includes the effects of inflation. It represents the percentage return an investor requires on their money without adjusting for the changes in purchasing power over time.
In financial modeling and investment valuation, cash flows are typically projected in nominal terms (meaning they include expected price increases). Therefore, to correctly calculate the Present Value (PV) of these cash flows, they must be discounted using a nominal rate.
Nominal vs. Real Discount Rates
The key difference between nominal and real rates lies in inflation:
- Real Discount Rate: The rate of return required excluding inflation. It reflects the pure time preference of money and risk premium.
- Nominal Discount Rate: The real rate plus an adjustment for expected inflation. This is the rate you see quoted in banks and bond markets.
How to Calculate Nominal Discount Rate
The most accurate way to convert a Real Discount Rate into a Nominal Discount Rate is using the Fisher Equation. While many people simply add the inflation rate to the real rate, the mathematically correct formula accounts for the compounding interaction between the two rates.
Formula:
(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)
Solved for Nominal Rate:
Nominal Rate = ((1 + Real Rate) × (1 + Inflation Rate)) – 1
Example Calculation
Imagine an investor requires a 5% real return (purchasing power increase) on an investment, and the economy is experiencing 3% inflation.
Using the linear approximation (Incorrect but common):
5% + 3% = 8.00%
Using the Fisher Equation (Correct):
1. Convert to decimals: 0.05 and 0.03
2. Multiply: (1.05) × (1.03) = 1.0815
3. Subtract 1: 1.0815 – 1 = 0.0815
4. Convert to percentage: 8.15%
The 0.15% difference represents the inflation eroding the value of the interest earned, a factor often overlooked in simple additions.
Why is this Important?
Using the wrong discount rate can significantly overvalue or undervalue an investment. If you project cash flows that include inflation (nominal cash flows) but discount them using a real rate, you will drastically overestimate the value of the asset.
- Rule of Thumb: Discount Nominal Cash Flows with a Nominal Discount Rate.
- Rule of Thumb: Discount Real Cash Flows (constant purchasing power) with a Real Discount Rate.