Bond Calculator

How this result is built

Price a fixed coupon bond from face value, coupon, yield, and payment frequency.

A bond price is the present value of its coupons plus the present value of the face amount, all discounted at the yield. When the yield is below the coupon, you pay more than face. When the yield is above the coupon, you pay less.

What the opening example is for

The quote assumes the next coupon is a full period away. A bond you buy between coupon dates has accrued interest on top of this clean price.

The walkthrough below uses the numbers already sitting in Bond Calculator. Press Calculate and the headline should match this page. Then put your own figures in. The math does not run until you press the button, and Clear hides the result.

What each field is doing

The “Face value” line on Bond Calculator starts at $1,000.00. A round example is useful for learning the page. It is a poor substitute for the number on your own paperwork, so replace it and run the form again.

Bond Calculator treats “Coupon rate” as its own entry, and the form opens with 5%. The other fields stay put while you change this one. That is the clean way to see what this line is doing inside the result.

Before you replace it, “Yield” reads 4.50% on Bond Calculator. If the label is a rate, type the annual figure the contract uses. If it is money, type the amount that will actually move, not a rounded hope.

The remaining fields

Look at “Years to maturity” first if you are checking Bond Calculator: the filled value is 10. Leave that figure only when it matches the statement, the quote, or the plan you are testing. Press Calculate after the edit so the chart and the schedule move with it.

The “Payments per year” line on Bond Calculator starts at 2. A round example is useful for learning the page. It is a poor substitute for the number on your own paperwork, so replace it and run the form again.

The opening result, line by line

Press Calculate on the opening form and Bond price is $1,039.91. That is the number the rest of this section is talking about.

Coupon each period is $25.00 when you run the opening figures on Bond Calculator. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

On this opening pass, premium / (discount) is $39.91. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

Bond Calculator reports that yield is 4.50%. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

How those lines were produced

Coupon rate is 5.00% when you run the opening figures on Bond Calculator. That line is part of the same calculation as the headline. It is not a second balance you can spend on top of the result. Change one input and press Calculate if you want to see whether this line moves.

When the yield is above the coupon, the price falls below face value.

The formula line on the page is Price = Σ Coupon/(1+y)^t + Face/(1+y)^n. It is there so you can see the relationship the buttons are using. A schedule, when the page draws one, is that same series written row by row.

A second pass changes only “Face value”, from $1,000.00 to $1,100.00. Bond price moves from $1,039.91 to $1,143.90. Nothing else on the form was edited, so the gap between those two results is the effect of that one field on Bond Calculator. If the gap is tiny, this page is not very sensitive to that entry. If the gap is large, get that entry from a document before you plan around the result.

What this page will not claim

Bond Calculator compounds the rate you type. Markets do not pay a flat rate, and a fund fee comes out of the return before you should type it. The page is the equation, not a forecast and not a recommendation to buy or sell.

Bond Calculator stops at its own formula. When the next question is different, open Present Value Calculator (What a future sum is worth today.); Interest Rate Calculator (The rate that makes the other four numbers true.); Investment Calculator (Starting balance plus a monthly contribution.). Do not add those results to this one as if they were the same kind of dollar.

Check the result before you use it

Start on Bond Calculator by reading the labels, not the headline. The opening labels are Face value ($1,000.00), Coupon rate (5%), Yield (4.50%), Years to maturity (10), Payments per year (2). If a label is not the fact you have, the result cannot turn into that fact later. The illustration on the form lands on $1,039.91. When you press Calculate and see that same figure, the button and this explanation are using one formula.

Change one field at a time. Write down the headline, edit a single line, and press Calculate again. A large jump means that line carries the result. A line that does not move is a line the formula ignores, which is a reason to confirm you opened the right page. Bond Calculator is built for one job: Price moves when the yield and the coupon disagree. The description on the page says the same thing in a sentence: Price a fixed coupon bond from face value, coupon, yield, and payment frequency.

When the paperwork disagrees

Then hold the headline next to a source outside the site. That source might be a loan estimate, an account statement, a pay stub, or the public limit named in the methodology. A few cents of difference on a long schedule is ordinary rounding. A different rate, a fee you never typed, or a tax the form does not ask for is not rounding. Correct the input. Do not average the page with the paperwork.

When the outside source still disagrees, Bond Calculator has reached the edge of what it will claim. It will not phone a lender, pull a county record, or apply a credit you left blank. Send the calculator name, every input, and the result you expected through the contact page if you think the formula itself is wrong. Until that is settled, read $1,039.91 as the output of the fields above and nothing else.

FAQs