Many investors think that because bonds pay a set amount of interest, they are risk-free investments. While it's true that bonds tend to be less volatile than stocks, there are still several risk factors investors should be aware of.

One major risk factor has to do with interest rate fluctuations. If interest rates rise or fall during the time you're holding a bond investment, it can have a big effect on the bond's market value. Here's a primer on determining bond values, and how you can determine what your bonds are worth today. Image source: Getty Images.

## What factors determine a bond's current value?

It often surprises new investors to learn that even though a bond will repay you \$1,000 upon reaching its maturity date, the market value of a bond can deviate quite a bit from this amount during its life cycle. There are four specific variables that determine a bond's value at any given time:

• Time to maturity: Prices of longer-maturity bonds tend to be more volatile than those maturing relatively sooner.
• Face value: For the vast majority of bonds, face value is \$1,000, although bonds can sometimes have different face values.
• Coupon interest rate: This is the interest rate the bond pays, based on its \$1,000 face value. For example, a \$1,000 bond that pays \$60 in annual interest would have a 6% coupon rate.
• Market interest rate: The current market interest rate for bonds of the same credit quality and duration. For example, if you want the current value of a 30-year Treasury, you need to use the current market yield of 30-year Treasurys when doing your calculations. If you're looking at AA-rated 10-year corporate bonds, be sure to use that rate.

## Now for the math part

Speaking of calculations, there are bond calculators that can do the hard part for you. A financial calculator, such as the HP 10bII I have sitting on my desk, can do the calculation, and there are several easy-to-use online bond calculators as well. So, if you're not mathematically inclined, don't worry.

Having said that, here's a look at the mathematical formula used to determine the current value of a bond, so you can understand where the value comes from: Image source: Author.

In the formula:

• "PMT" stands for the dollar amount of each interest payment
• "i" stands for the current market interest rate, expressed as a decimal (e.g., 7% would be 0.07)
• "c" stands for the number of interest payments per year (usually two)
• "n" stands for the number of years until maturity

In other words, the current value of a bond is the present value of its interest payments plus its eventual principal repayment.

As you can see, this is quite a complex formula, especially if your bond has more than a couple years until maturity, so it's generally best to use a calculator to figure out how much your bonds are worth.

## An example

Let's say that you bought a 30-year Treasury bond in 2010 with a coupon rate of 4.75%. So the bond pays you \$47.50 per year and will repay your initial \$1,000 principal in 2040.

As of this writing, the 30-year Treasury yield (market interest rate) is about 3.15%. Your bond now has 22 years until maturity, so using a financial calculator shows a current value of \$1,253. This would be (roughly) what you could expect if you decided to sell the bond on the open market.

## How to use this

Knowing how to determine bond values is useful for three main situations:

1. So you don't overpay for bonds. Many bonds -- especially corporate bonds -- aren't terribly liquid, meaning that there's a small market for them. Knowing how to use these variables to determine a bond's market value helps ensure that you'll pay a fair price.
2. To determine how much you could sell your bonds for. As we saw in the example, if market interest rates have fallen since you bought your bonds, they can be worth significantly more than you paid. Conversely, if market interest rates have risen, your bonds can be worth much less.
3. To see what could happen to your bond values. This can be especially useful in the current rising-rate environment. If bond yields jump by another 1% or more, what would it mean to you? This calculation can help you find out.