# Bond Value CalculatorCalculate and Learn Valuation/Pricing

Discover the price a bond should be selling for. See the formula used with an example. Learn how to calculate the price for yourself.

This free online Bond Value Calculator will calculate the expected trading price of a bond given the par value, coupon rate, market rate, interest payments per year, and years-to-maturity.

Plus, the calculated results will show the step-by-step solution to the bond valuation formula, as well as a chart showing the present values of the par value and each coupon payment.

If you don't know the answer to the questions, "What are bonds?", or "How do bonds work?", be sure to visit the Yield to Maturity Calculator page that includes a basic definition of bonds and a brief explanation of how they work.

### What is Bond Valuation?

Bond valuation is a method used to determine the expected trading price of a bond. The expected trading price is calculated by adding the sum of the present values of all coupon payments to the present value of the par value (no worries, the bond value calculator on this page performs all of the calculations for you, and shows its work).

### How To Calculate The Value of a Bond

Since the value of a bond is equal to the sum of the present values of the par value and all of the coupon payments, we can use the Present Value of An Ordinary Annuity Formula to find the value of a bond (as generated by the Bond Valuation Calculator lower down on this page).

#### Bond Valuation Example

Suppose XYZ issues ten-year bonds (par value of \$1,000.00) with an annual coupon rate of 10% and paying interest semi-annually. Similar 10-year bonds are paying 12% interest. What is the value of one of XYZ's new bonds? In other words, what should the price be?

 Variables C = coupon payment = \$100.00 (Par Value * Coupon Rate) n = number of years = 10 i = market rate, or required yield = 12.000% = 0.12 k = number of coupon payments in 1 year = 2 P = value at maturity, or par value = 1000
Present Value of Ordinary Annuity Formula
Bond Price = C/k *
 [ 1 - [ 1 ] ] (1 + i/k)nk i/k
+
 P (1 + i/k)nk
Plug In The Variables and Solve
Bond Price = 100/2 *
 [ 1 - [ 1 ] ] (1 + 0.12/2)10*2 0.12/2
+
 1000 (1 + 0.12/2)10*2
Bond Price = 50 *
 [ 1 - [ 1 ] ] (1 + 0.06)20 0.06
+
 1000 (1 + 0.06)20
Bond Price = 50 *
 [ 1 - [ 1 ] ] 3.207 0.06
+
 1000 3.207
Bond Price = 50 *
 1 - 0.3118 0.06
+
 1000 3.207
Bond Price = 50 *
 0.6882 0.06
+311.80
 Bond Price = 50 * 11.47 + 311.8
 Bond Price = 573.5 + 311.8
 Bond Price = \$885.30

You can also find the bond price using a spreadsheet to calculate and sum the present values of the par value and all of the coupon payments, like this:

 End of Year Interest Principal Present Value 0.50 \$50.00 \$47.17 1.00 \$50.00 \$44.50 1.50 \$50.00 \$41.98 2.00 \$50.00 \$39.60 2.50 \$50.00 \$37.36 3.00 \$50.00 \$35.25 3.50 \$50.00 \$33.25 4.00 \$50.00 \$31.37 4.50 \$50.00 \$29.59 5.00 \$50.00 \$27.92 5.50 \$50.00 \$26.34 6.00 \$50.00 \$24.85 6.50 \$50.00 \$23.44 7.00 \$50.00 \$22.12 7.50 \$50.00 \$20.86 8.00 \$50.00 \$19.68 8.50 \$50.00 \$18.57 9.00 \$50.00 \$17.52 9.50 \$50.00 \$16.53 10.00 \$50.00 \$15.59 10.00 \$1,000.00 \$311.80 TOTAL \$885.30

### Why Do Bond Prices Change?

Since the price of bonds trend in the opposite direction of interest rates, the price an investor is willing to pay for bonds tends to decrease as interest rates rise, and increase as interest rates decline. If this sounds confusing to you, perhaps a simple example will help clear the air.

### Why Bond Prices and Interest Rates Move In Opposite Directions

To illustrate why bond prices and market interest rates tend to move in opposite directions, suppose you purchased a 5-year, \$1,000 bond at face value that was paying a 7% coupon rate.

Now, suppose market interest rates rise, thereby causing bonds similar to yours to offer, say, an 8% coupon rate. If you were looking to sell your 7% bond, you would need to discount the price of your bond to the point where the buyer would achieve the same total return being offered by the bond paying 8%. Using the bond valuation formula that's built into the bond value calculator, we can determine that an investor would need to be able to purchase your \$1,000 bond for \$960.07 in order to get the same total return as the one paying 8%.

On the other hand, suppose market interest rates fall, thereby causing bonds similar to yours to offer only a 6% coupon rate. If you were looking to sell your 7% bond, your bond is obviously worth more than bonds paying only 6%. In this case, using the bond valuation formula that's built into the bond value calculator, we can see that an investor should be willing to purchase your \$1,000 bond for \$1,042.12, as that price would still net the investor the same total return as the one paying 6%.

Those two examples should help to explain why interest rates have an inverse relationship with bond prices. And it's a good thing they have this inverse relationship.

### The Function of Price Fluctuations

The underlying reason bond prices rise and fall is to bring the rates of older bonds into line with prevailing rates. Were it not for these price fluctuations, there would be no liquidity in the bonds market and very few issuers. After all, no one would be willing to buy bonds at par value if the bonds were paying lower interest rates than the prevailing rates, and issuers would not issue bonds if doing so would cause them to pay a higher interest rate than if they were to borrow the money elsewhere.

### Maturities and the Effects of Interest Rate Changes

The more you use the bond value calculator, the more it should become clear that the effects that changing interest rates have on the price of a bond tend to become less and less the closer it gets to its maturity date. This is because the interest rate risk (risk of missing out on higher interest rates) decreases the closer bonds get to their maturity dates.

With that, let's use the Bond Value Calculator to calculate the price of a bond given its face value, coupon rate, market rate, and years-to-maturity.

Bond Value Calculator

Instructions: Enter the par value, enter the coupon rate, and select the coupon rate compounding frequency.

Next enter the current market rate and the number of years to maturity, then click the "Calculate Bond Price" button.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Bond Value Calculator.

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Par value (\$):
Coupon rate (%):
Coupon rate compounding interval:
Current market rate of similar bonds (%):
Years to maturity (#):
Bond value:
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### Bond Value Calculator Glossary of Terms

Par value: Par value is also referred to as the face value, both of which refer to the amount the bond issuer promises to pay the bond holder on the maturity date.

Coupon rate: The coupon rate is the annual interest the bond pays. If a bond with a par value of \$1,000 is paying you \$80 per year, then the coupon rate would be 8% (80 ÷ 1000 = .08, or 8%).

Coupon rate compounding interval: Select the compounding frequency of the coupon rate. Typically, the shorter the compounding interval, the more interest you will earn with all other factors remaining the same. While the effects of compounding are fairly insignificant for small investments, the effects can be very significant when investing a large sum of money.

Current market rate: The current market rate that similar bonds are selling for. If the current market rate is below the coupon rate, then the bond should be trading at a premium (price greater than the par value). Conversely, if the current market rate is above the coupon rate, then the bond should be selling at a discount (price less than par value).

Years to maturity: The number of years remaining before the bond reaches its maturity date. The maturity of a bond is the year the par or face value of the bond is returned to the bond holder.

Bond value: Given the face value, coupon rate, coupon compounding interval, years to maturity, and the current market rate, this is the price the bond should be trading at. In other words, this should be the price a buyer would be willing to pay to purchase the bond.

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