US Bonds, issued by the U.S. Department of the Treasury, are considered among the safest investments in the world. They are debt instruments used by the government to finance its operations. When you buy a US Bond, you are essentially lending money to the government for a specified period, and in return, you receive periodic interest payments (coupon payments) and the return of your principal amount at maturity.
How This Calculator Works:
This calculator helps you estimate the fair market price of a bond and understand the relationship between a bond's coupon rate, its maturity, and the prevailing market interest rates (yield).
Bond Price Calculation:
The fair market price of a bond is the present value of all its future cash flows, discounted at the current market yield. The future cash flows consist of:
Periodic coupon payments (interest payments)
The face value (principal) paid back at maturity
The formula used is:
Bond Price = ∑ [ Coupon Payment / (1 + Yield/n)^(n*t) ] + [ Face Value / (1 + Yield/n)^(n*T) ]
Where:
Coupon Payment: (Face Value * Coupon Rate) / n
Yield: Current Market Yield (annualized)
n: Number of coupon payments per year (assumed to be 1 for simplicity in this calculator, representing annual payments)
t: The number of periods from the present until the coupon payment occurs (t = 1, 2, …, T)
T: Total number of periods until maturity
Face Value: The principal amount repaid at maturity
For annual coupon payments (n=1):
Bond Price = ∑ [ (Face Value * Coupon Rate) / (1 + Yield)^t ] (for t from 1 to Years to Maturity) + [ Face Value / (1 + Yield)^Years to Maturity ]
Relationship between Price and Yield:
Inverse Relationship: When market interest rates (yields) rise, newly issued bonds offer higher coupon payments. To remain competitive, existing bonds must trade at a discount (below face value) to attract buyers. Conversely, when market yields fall, existing bonds with higher coupon rates become more attractive and trade at a premium (above face value).
Par Value: If the current market yield is equal to the bond's coupon rate, the bond will trade at its face value (par value).
If the current market yield for similar bonds is 4.5% (lower than the coupon rate), investors will find your bond attractive. They will be willing to pay more than $1,000 for it, as it offers a higher interest payment than new bonds in the market. The calculator will show a price above $1,000.
Conversely, if the current market yield rises to 5.5% (higher than the coupon rate), new bonds will offer better returns. Your bond will become less attractive, and its price will fall below $1,000 to compensate investors for the lower coupon payments. The calculator will show a price below $1,000.
Use Cases for This Calculator:
Investors: Understand the current market value of bonds they own or are considering purchasing.
Financial Advisors: Educate clients on bond pricing and the impact of interest rate changes.
Students: Learn the fundamentals of bond valuation and fixed-income mathematics.
Portfolio Management: Assess the impact of changing market yields on bond holdings.
function calculateBondPrice() {
var faceValue = parseFloat(document.getElementById("faceValue").value);
var couponRate = parseFloat(document.getElementById("couponRate").value);
var yearsToMaturity = parseFloat(document.getElementById("yearsToMaturity").value);
var currentMarketYield = parseFloat(document.getElementById("currentMarketYield").value);
var resultDiv = document.getElementById("bondPriceResult");
var yieldResultDiv = document.getElementById("bondYieldResult");
var errorDiv = document.getElementById("errorMessage");
// Clear previous results and errors
resultDiv.innerHTML = ";
yieldResultDiv.innerHTML = ";
yieldResultDiv.style.display = 'none';
errorDiv.innerHTML = ";
// Input validation
if (isNaN(faceValue) || faceValue <= 0) {
errorDiv.innerHTML = "Please enter a valid positive Face Value.";
return;
}
if (isNaN(couponRate) || couponRate < 0) {
errorDiv.innerHTML = "Please enter a valid non-negative Coupon Rate.";
return;
}
if (isNaN(yearsToMaturity) || yearsToMaturity <= 0) {
errorDiv.innerHTML = "Please enter a valid positive number of Years to Maturity.";
return;
}
if (isNaN(currentMarketYield) || currentMarketYield < 0) {
errorDiv.innerHTML = "Please enter a valid non-negative Current Market Yield.";
return;
}
// Assuming annual coupon payments (n=1)
var n = 1;
var couponPayment = (faceValue * couponRate) / 100;
var annualYieldRate = currentMarketYield / 100;
var bondPrice = 0;
// Calculate the present value of future cash flows
for (var t = 1; t currentMarketYield) {
yieldResultDiv.innerHTML = "This bond is trading at a premium (above Face Value) because its coupon rate is higher than the current market yield.";
yieldResultDiv.style.display = 'block';
} else if (couponRate < currentMarketYield) {
yieldResultDiv.innerHTML = "This bond is trading at a discount (below Face Value) because its coupon rate is lower than the current market yield.";
yieldResultDiv.style.display = 'block';
} else {
yieldResultDiv.innerHTML = "This bond is trading at par (equal to Face Value) because its coupon rate matches the current market yield.";
yieldResultDiv.style.display = 'block';
}
}