The actual purchasing power growth you want to achieve.
%
The expected rate at which prices will rise.
Approximate Nominal Rate:0.00%
Exact Nominal Rate (Fisher):0.00%
Rate Premium Required:0.00%
function calculateFisherEffect() {
// Get input values
var realRateInput = document.getElementById('nrc_real_rate').value;
var inflationRateInput = document.getElementById('nrc_inflation_rate').value;
// Validate inputs
if (realRateInput === "" || inflationRateInput === "") {
alert("Please enter both the Real Interest Rate and the Inflation Rate.");
return;
}
var realRate = parseFloat(realRateInput);
var inflationRate = parseFloat(inflationRateInput);
if (isNaN(realRate) || isNaN(inflationRate)) {
alert("Please enter valid numerical values.");
return;
}
// Calculation Logic based on Fisher Equation: (1 + i) = (1 + r) * (1 + π)
// i = Nominal Rate
// r = Real Rate
// π = Inflation Rate
// Convert percentages to decimals
var r = realRate / 100;
var pi = inflationRate / 100;
// Exact Formula: i = ((1 + r) * (1 + pi)) – 1
var exactNominalDecimal = ((1 + r) * (1 + pi)) – 1;
var exactNominalPercent = exactNominalDecimal * 100;
// Approximate Formula: i ≈ r + pi
var approxNominalPercent = realRate + inflationRate;
// Difference (Inflation Premium compounding effect)
var difference = exactNominalPercent – approxNominalPercent;
// Display Results
var resultBox = document.getElementById('nrc_result_box');
var exactDisplay = document.getElementById('nrc_exact_result');
var approxDisplay = document.getElementById('nrc_approx_result');
var premiumDisplay = document.getElementById('nrc_premium');
exactDisplay.innerHTML = exactNominalPercent.toFixed(4) + "%";
approxDisplay.innerHTML = approxNominalPercent.toFixed(2) + "%";
// Show the difference logic
premiumDisplay.innerHTML = "+" + difference.toFixed(4) + "% (Compounding Effect)";
resultBox.style.display = "block";
}
Understanding the Nominal Rate and Inflation
In economics and finance, distinguishing between the numbers you see on a bank statement (nominal rates) and the actual value those numbers represent (real rates) is crucial. This Nominal Rate Calculator helps you determine the interest rate required to achieve a specific increase in purchasing power, accounting for the erosion of value caused by inflation.
What is the Nominal Interest Rate?
The nominal interest rate is the percentage increase in money that the borrower pays to the lender. It is the "advertised" rate. For example, if a savings account offers a 5% annual yield, 5% is the nominal rate. However, this number does not account for what that money can actually buy in the future.
What is the Real Interest Rate?
The real interest rate represents the growth of your purchasing power. It strips out the effects of inflation. If your savings account grows by 5% (nominal), but the prices of goods and services rise by 3% (inflation), your real purchasing power has only grown by roughly 2%.
The Fisher Equation
To accurately calculate the relationship between these rates, economists use the Fisher Equation. While many people simply add the real rate and inflation rate together (the approximation), the exact formula accounts for the compounding effect of inflation on the interest itself.
The formula used in this calculator is:
(1 + i) = (1 + r) × (1 + π)
i = Nominal Interest Rate
r = Real Interest Rate
π = Inflation Rate
Solving for the Nominal Rate (i): i = ((1 + r) × (1 + π)) – 1
Why the "Approximate" Method is Often Wrong
A common rule of thumb is: Nominal ≈ Real + Inflation.
While this works well for low rates, the error margin increases as rates get higher. For example:
Scenario: You want a 10% return in purchasing power (Real Rate) and inflation is 50% (Hyperinflation).