Bond Pricing

Purpose

This calculator estimates the fair price of a bond today, given its face value, its coupon rate, how often it pays interest, how long until it matures, and the prevailing market interest rate. It is useful for investors and analysts who want to know what a bond is worth based on discounting its future coupon payments and final repayment at a current market rate.

Background

Why a bond's price can differ from its face value

A bond promises to pay a series of fixed coupon payments and then repay its Face Value at maturity. Its price today is the present value of those future payments, discounted at the prevailing Interest Rate for a bond of similar risk and maturity. When the Coupon Rate equals the Interest Rate, the bond prices at (or very near) its face value. When the Coupon Rate is higher than the Interest Rate, the bond is worth more than its face value (it trades at a premium), because it pays more than the market currently requires. When the Coupon Rate is lower than the Interest Rate, the bond is worth less than face value (it trades at a discount).

Inputs

Face Value

The amount the bond repays at maturity, and the amount its coupon payments are calculated on.

Coupon Rate

The bond's stated annual interest rate, used to calculate each coupon payment. Enter it as a rate per year (for example, 5 pct/yr).

Interest Payment Interval

How often coupon payments are made — for example, every half year, quarter, or year. This determines both the size of each coupon payment (the annual Coupon Rate is applied proportionally to the length of the interval) and how many payments occur before maturity.

Duration

The time remaining until the bond matures, entered with a time unit (for example, 2 yr). Together with Interest Payment Interval, this determines the total number of coupon payments.

Interest Rate

The prevailing annual market interest rate used to discount the bond's future payments back to today's value. Like Coupon Rate, it is entered as a rate per year and applied proportionally to each payment interval.

Results

Bond Price

The estimated fair price of the bond today: the present value of all coupon payments plus the present value of the face value repaid at maturity, discounted at the Interest Rate. Compare this to the Face Value to see whether the bond prices at a premium (Bond Price above Face Value), at a discount (Bond Price below Face Value), or at par (Bond Price close to Face Value).

Understanding the Calculation

The annual Coupon Rate and Interest Rate are each converted to a per-period rate by multiplying by the length of one Interest Payment Interval (for example, an annual rate applied over a half-year interval gives half the annual rate per period). The number of payment periods is the Duration divided by the Interest Payment Interval.

For each period from 1 to the total number of periods, the coupon payment (Coupon Rate per period × Face Value) is discounted back to today using the per-period Interest Rate:

$$\text{Bond Price} = \sum_{i=1}^{n} \dfrac{\text{Coupon Rate} \times \text{Face Value}}{(1+\text{Interest Rate})^{i}} \;+\; \dfrac{\text{Face Value}}{(1+\text{Interest Rate})^{n}}$$

where both rates are per-period values and $n$ is the total number of payment periods. The last term discounts the return of the Face Value itself at maturity.

Example

Using the default inputs — a Face Value of 1000, a Coupon Rate of 5% per year, interest paid every half year, a Duration of 2 years (4 half-year periods), and an Interest Rate of 3% per year — the calculator returns a Bond Price of approximately 1038.54. Since the 5% Coupon Rate exceeds the 3% Interest Rate, the bond is worth more than its 1000 Face Value — it trades at a premium of about 38.54.

For comparison, if the Coupon Rate and Interest Rate are both set to 3% (all other inputs unchanged), the Bond Price comes out to essentially 1000 — the bond prices at par, as expected when the coupon exactly matches the market rate.

Important Assumptions and Interpretation

• The calculation assumes coupon payments are made exactly on schedule at the stated Interest Payment Interval, with no missed or irregular payments, and no default risk.
• The Interest Rate used for discounting is assumed constant over the entire remaining Duration; it does not model a changing yield curve.
• Duration should divide evenly by the Interest Payment Interval for a whole number of payment periods; check both inputs use consistent time units.
• The result is an estimated fair price based on the inputs given, not a quoted market price, which can also be affected by liquidity, credit risk, and other market factors not modeled here.