# Yield Calculation for a 10-Year Treasury Note

The U.S. 10-year Treasury note is the benchmark for U.S. interest rates, as it is the most liquid, heavily-traded debt security issued by the federal government. Just like stock investors turn to the Dow Jones Industrial Average or the S&P 500 Index to gauge how the U.S. stock market is performing, bond investors watch the rise and fall of the 10-year Treasury note to interpret how the interest rate market is doing. The yield for the 10-year note, which initially is set at auction, ultimately is determined in the open market by buyers and sellers.

## Initial Rate

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Ten-year Treasuries come to market via a government auction. Yields are set by supply and demand. When demand for a note is high, the yield falls; conversely, if there is low demand at auction, the yield will increase. After the price and yield are set at auction, individual buyers are free to buy or sell bonds in the open market.

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## Market Rate

After a bond's price is determined at auction, the bonds trade in the secondary market. Bonds purchased in the secondary market may have yields higher or lower than their auction rate, based on supply and demand as well as other factors, such as broker commission. Time also is a factor in the secondary market, as bonds have fixed maturity dates. As each day elapses, the time to maturity for a bond shortens, which typically also reduces its yield.

## Types of Yield Calculations

When evaluating at a bond, there are two primary yield calculations: the current yield and the yield to maturity. Current yield simply is the annual interest amount that a bond pays divided by the current price of the bond. For example, if you buy a bond with a \$1,000 face value and an interest rate -- also known as the coupon rate -- of three percent, you'll earn \$30 per year in interest.

If the price of the bond is \$1,000, your current yield also is three percent. However, if the bond has fallen in value to \$900, then your current yield is 3.33 percent, or \$30 divided by \$900. If the price has rise to \$1,100, your current yield falls to 2.73 percent.

Yield to maturity is a more complex calculation that attempts to incorporate the total return an investor will receive from the time of purchase to maturity, including interest payments, the rise or fall in the price of the bond and the reinvestment of interest. For example, if you buy a 4-percent bond at par value, or \$1,000, your yield to maturity also will be 4 percent, as there will be no change in the price of the bond at maturity. However, if you buy a bond for \$900, you'll receive your annual four percent coupon plus an additional \$100 at maturity. The formula for the yield to maturity calculation is:

Where:

P = price of the bond
n = number of periods
C = coupon payment
r = required rate of return on this investment
F = maturity value
t = time period when payment is to be received

Since the mathematics can be daunting even for expert investors, numerous financial calculators and websites can calculate yield to maturity for you -- as long as you know the bond's par value, interest rate, current price, number of payments per year and time to maturity.