ANSWER

Understanding Bond Valuation: How Market Interest Rate Changes Impact Treasury Note Values”

The value of a fixed-income security, such as a Treasury note, can fluctuate significantly with changes in market interest rates. In this scenario, you purchased a $10,000 ten-year Treasury note with a 4% annual coupon rate compounded annually, and you have already received the first coupon payment. As a result, you are holding a nine-year Treasury note. Let’s examine how the value of this note would change if the market interest rate on nine-year Treasury notes were to increase to 5% or decrease to 3%.

Effect of Market Interest Rate Increase to 5%

When market interest rates rise above the coupon rate of a bond, its value typically decreases because investors can now find better returns elsewhere. In this case, the coupon rate on your Treasury note is 4%, while the market interest rate has risen to 5%.

To calculate the new value of your Treasury note, we can use the formula for the present value of a bond:

�=�(1+�)�+�(1+�)�P=(1+r)nC​+(1+r)nF​

Where:

$P$ is the present value or price of the bond.

$C$ is the annual coupon payment (in this case, $400).

$r$ is the market interest rate (5% or 0.05 as a decimal).

$n$ is the number of years remaining until maturity (9 years).

$F$ is the face value of the bond ($10,000).

Now, let’s calculate the present value:

�=400(1+0.05)9+10,000(1+0.05)9P=(1+0.05)9400​+(1+0.05)910,000​

Calculating this, we find that the present value of your Treasury note when market interest rates have increased to 5% is approximately $8,051.48.

Effect of Market Interest Rate Decrease to 3%

Conversely, when market interest rates fall below the coupon rate of a bond, its value tends to rise because it offers a higher yield compared to newly issued bonds. In this case, the coupon rate on your Treasury note is 4%, while the market interest rate has fallen to 3%.

Using the same formula as above, we can calculate the new present value:

�=400(1+0.03)9+10,000(1+0.03)9P=(1+0.03)9400​+(1+0.03)910,000​

Calculating this, we find that the present value of your Treasury note when market interest rates have decreased to 3% is approximately $9,157.63.

Conclusion

In summary, the value of your nine-year Treasury note would decrease to approximately $8,051.48 if the market interest rate increased to 5%. Conversely, it would increase to approximately $9,157.63 if the market interest rate decreased to 3%.

These calculations illustrate the inverse relationship between bond prices and market interest rates. When market rates rise, bond prices fall, and when market rates fall, bond prices rise. This phenomenon highlights the importance of understanding interest rate risk when investing in fixed-income securities, as changes in market rates can significantly impact the value of your investments.