The price of a bond is the present value of all its future cash flows, discounted at the prevailing market interest rate (Yield to Maturity or YTM). These future cash flows consist of periodic coupon payments and the final repayment of the bond's face value (par value) at maturity.
The Formula
The price of a bond can be calculated using the following formula:
C = Periodic Coupon Payment (Annual Coupon Rate * Face Value) / Coupon Frequency
FV = Face Value (Par Value) of the bond
y = Market Yield (Yield to Maturity – YTM) per period. This is calculated as Annual Market Yield / Coupon Frequency.
n = Total number of coupon periods until maturity. This is calculated as Years to Maturity * Coupon Frequency.
This formula essentially sums up the present value of each coupon payment and the present value of the face value received at maturity.
How the Calculator Works
Our Bond Pricing Calculator takes the following inputs:
Face Value (Par Value): The nominal amount of money the bond issuer will repay the bondholder at maturity. This is usually $1,000 or $100.
Annual Coupon Rate: The fixed interest rate the bond pays annually, expressed as a percentage of the face value.
Years to Maturity: The remaining time until the bond's principal is repaid.
Market Yield (YTM): The total return anticipated on a bond if the bond is held until it matures. This is the discount rate used to calculate the bond's present value. It fluctuates with market conditions.
Coupon Payments Per Year: How often the coupon interest is paid (e.g., annually, semi-annually, quarterly, monthly).
The calculator then applies the bond pricing formula to compute the bond's current market price.
Interpreting the Results
The calculated bond price will indicate:
If Bond Price = Face Value: The bond is trading at par. This typically occurs when the Market Yield (YTM) is equal to the Coupon Rate.
If Bond Price > Face Value: The bond is trading at a premium. This occurs when the Market Yield (YTM) is lower than the Coupon Rate, meaning investors are willing to pay more for the higher coupon payments.
If Bond Price < Face Value: The bond is trading at a discount. This occurs when the Market Yield (YTM) is higher than the Coupon Rate, meaning investors require a higher yield than the bond's coupon rate, thus paying less for it.
Use Cases
This calculator is useful for:
Investors evaluating potential bond purchases.
Financial analysts determining the fair value of bonds.
Understanding the relationship between interest rates, coupon payments, and bond prices.
Educating individuals on fixed-income securities.
function calculateBondPrice() {
var faceValue = parseFloat(document.getElementById("faceValue").value);
var couponRate = parseFloat(document.getElementById("couponRate").value);
var maturityYears = parseFloat(document.getElementById("maturityYears").value);
var marketYield = parseFloat(document.getElementById("marketYield").value);
var couponFrequency = parseInt(document.getElementById("couponFrequency").value);
var resultDiv = document.getElementById("bondPriceResult");
var resultValueDiv = document.getElementById("bondPriceResultValue");
// Clear previous results
resultDiv.innerText = "–";
resultValueDiv.innerText = "";
// Input validation
if (isNaN(faceValue) || faceValue <= 0 ||
isNaN(couponRate) || couponRate < 0 ||
isNaN(maturityYears) || maturityYears <= 0 ||
isNaN(marketYield) || marketYield < 0 ||
isNaN(couponFrequency) || couponFrequency <= 0) {
resultDiv.innerText = "Error";
resultValueDiv.innerText = "Please enter valid positive numbers for all fields.";
return;
}
// Convert annual rates to per-period rates
var periodicCouponRate = (couponRate / 100) / couponFrequency;
var periodicMarketYield = marketYield / 100 / couponFrequency;
var numberOfPeriods = maturityYears * couponFrequency;
// Calculate periodic coupon payment
var couponPayment = (faceValue * periodicCouponRate);
var bondPrice = 0;
// Calculate the present value of coupon payments (Annuity)
if (periodicMarketYield === 0) {
// If yield is 0, present value of annuity is simply payment * number of periods
bondPrice = couponPayment * numberOfPeriods;
} else {
// PV of annuity formula: C * [1 – (1 + y)^-n] / y
bondPrice = couponPayment * (1 – Math.pow(1 + periodicMarketYield, -numberOfPeriods)) / periodicMarketYield;
}
// Calculate the present value of the face value (Lump Sum)
var pvFaceValue = faceValue / Math.pow(1 + periodicMarketYield, numberOfPeriods);
// Total bond price is the sum of PV of coupons and PV of face value
bondPrice += pvFaceValue;
// Format the result
var formattedPrice = bondPrice.toLocaleString(undefined, {
minimumFractionDigits: 2,
maximumFractionDigits: 2
});
resultDiv.innerText = "$" + formattedPrice;
resultValueDiv.innerText = "The calculated price of the bond based on current market yields.";
}