.calculator-container {
max-width: 800px;
margin: 0 auto;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
color: #333;
line-height: 1.6;
}
.calc-box {
background: #f8f9fa;
border: 1px solid #e9ecef;
border-radius: 8px;
padding: 30px;
margin-bottom: 40px;
box-shadow: 0 4px 6px rgba(0,0,0,0.05);
}
.calc-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
}
.input-group label {
font-weight: 600;
margin-bottom: 5px;
font-size: 0.9em;
color: #495057;
}
.input-group input, .input-group select {
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
}
.input-group input:focus, .input-group select:focus {
border-color: #80bdff;
outline: 0;
box-shadow: 0 0 0 0.2rem rgba(0,123,255,.25);
}
.calc-btn {
grid-column: 1 / -1;
background-color: #007bff;
color: white;
border: none;
padding: 12px;
font-size: 18px;
font-weight: bold;
border-radius: 4px;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #0056b3;
}
.result-box {
grid-column: 1 / -1;
background: #ffffff;
border: 1px solid #dee2e6;
padding: 20px;
border-radius: 4px;
margin-top: 20px;
display: none;
}
.result-box.visible {
display: block;
}
.result-row {
display: flex;
justify-content: space-between;
align-items: center;
padding: 10px 0;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #6c757d;
}
.result-value {
font-weight: 700;
font-size: 1.2em;
color: #28a745;
}
.article-content h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
.article-content p {
margin-bottom: 15px;
}
.article-content ul {
margin-bottom: 15px;
padding-left: 20px;
}
.formula-box {
background: #eef2f7;
padding: 15px;
border-left: 4px solid #007bff;
font-family: monospace;
margin: 20px 0;
}
@media (max-width: 600px) {
.calc-grid {
grid-template-columns: 1fr;
}
}
function calculateEquivalentRate() {
// 1. Get Inputs
var baseRateInput = document.getElementById('baseRate').value;
var baseFreq = parseFloat(document.getElementById('baseFrequency').value);
var targetFreq = parseFloat(document.getElementById('targetFrequency').value);
var principalInput = document.getElementById('principal').value;
// 2. Validation
if (baseRateInput === "" || isNaN(baseRateInput)) {
alert("Please enter a valid Base Nominal Rate.");
return;
}
var r = parseFloat(baseRateInput) / 100; // Convert percentage to decimal
var p = (principalInput === "" || isNaN(principalInput)) ? 1000 : parseFloat(principalInput);
var ear = 0;
var targetRate = 0;
// 3. Logic: Calculate EAR (Effective Annual Rate) first
// Formula: EAR = (1 + r/n)^n – 1 (Discrete)
// Formula: EAR = e^r – 1 (Continuous)
if (baseFreq === 0) {
// Continuous compounding for base
ear = Math.exp(r) – 1;
} else {
// Discrete compounding for base
ear = Math.pow((1 + (r / baseFreq)), baseFreq) – 1;
}
// 4. Logic: Convert EAR to Target Rate
// Formula: r_target = n * ((1 + EAR)^(1/n) – 1) (Discrete)
// Formula: r_target = ln(1 + EAR) (Continuous)
if (targetFreq === 0) {
// Target is Continuous
targetRate = Math.log(1 + ear);
} else {
// Target is Discrete
targetRate = targetFreq * (Math.pow((1 + ear), (1 / targetFreq)) – 1);
}
// 5. Calculate Yield check (Value after 1 year)
var futureValue = p * (1 + ear);
var interestEarned = futureValue – p;
// 6. Display Results
var earPercentage = (ear * 100).toFixed(4) + "%";
var targetPercentage = (targetRate * 100).toFixed(4) + "%";
var yieldText = p.toFixed(2) + " grows to " + futureValue.toFixed(2);
document.getElementById('displayEAR').innerHTML = earPercentage;
document.getElementById('displayTargetRate').innerHTML = targetPercentage;
document.getElementById('displayYield').innerHTML = yieldText;
// Update Label to be specific
var freqMap = {
"1": "Annually", "2": "Semi-Annually", "4": "Quarterly",
"12": "Monthly", "24": "Semi-Monthly", "26": "Bi-Weekly",
"52": "Weekly", "365": "Daily", "0": "Continuously"
};
var targetName = freqMap[targetFreq.toString()];
document.getElementById('targetLabel').innerHTML = "Rate Compounded " + targetName + ":";
document.getElementById('resultBox').className = "result-box visible";
}
Equivalent Rate Converter
Annually (1/yr)
Semi-Annually (2/yr)
Quarterly (4/yr)
Monthly (12/yr)
Semi-Monthly (24/yr)
Bi-Weekly (26/yr)
Weekly (52/yr)
Daily (365/yr)
Continuous
Annually (1/yr)
Semi-Annually (2/yr)
Quarterly (4/yr)
Monthly (12/yr)
Semi-Monthly (24/yr)
Bi-Weekly (26/yr)
Weekly (52/yr)
Daily (365/yr)
Continuous
Base Effective Annual Rate (EAR):
–
Target Equivalent Rate:
–
Yield Difference (over 1 year):
–
Understanding Equivalent Rates
In the world of finance and mathematics, the Equivalent Rate refers to the adjustment required to compare interest rates or yields that have different compounding periods. A nominal rate of 10% compounded monthly is not mathematically equal to 10% compounded annually due to the effect of compound interest.
This Equivalent Rate Calculator allows you to convert a nominal rate with one compounding frequency (e.g., Monthly) into an equivalent nominal rate with a different frequency (e.g., Daily or Annually), such that the Effective Annual Rate (EAR) remains constant.
Why Compounding Frequency Matters
When interest is compounded more frequently, the effective yield increases. For example, if you have a 12% annual rate:
- Compounded Annually: You earn 12% at the end of the year.
- Compounded Monthly: You earn 1% each month. Because the interest from the first month earns its own interest in the second month, the total yield at the end of the year is actually higher than 12%.
To equate these two scenarios, the nominal rate for the more frequent compounding period must be lower to achieve the same final outcome.
How to Use This Calculator
- Enter Base Nominal Rate: Input the percentage rate you currently have or are analyzing.
- Select Base Frequency: Choose how often this rate is compounded (e.g., Monthly for a standard savings account).
- Select Target Frequency: Choose the compounding period you want to convert to (e.g., Annually to find the APY/EAR, or Daily).
- Reference Amount: Optionally, enter a principal amount to see how the math affects a real balance over one year.
The Mathematics of Equivalence
The calculation relies on equating the Effective Annual Rate (EAR) of both scenarios.
(1 + r1/n1)^(n1) = (1 + r2/n2)^(n2)
Where:
- r1, r2: The nominal interest rates (as decimals).
- n1, n2: The number of compounding periods per year.
To solve for the target rate (r2), the formula is rearranged:
r2 = n2 * [ ( (1 + r1/n1)^(n1/n2) ) – 1 ]
Common Applications
This tool is essential for:
- Comparing Loans: A mortgage compounded semi-annually (common in Canada) versus a mortgage compounded monthly (common in the US).
- Investment Analysis: Comparing a bond that pays semi-annually against a savings account that pays monthly.
- Legal & Accounting: Converting contractual rates to standardized effective rates for compliance.