Question

We have discussed how to calculate the yield to maturity for a fixed-payment loan. Now, we can applied the process to find the interest for a bond. Consider a $1,000-face-value bond with 5 years to maturity and yearly coupon payments of $100, which means you will receive $100 every year for the next five years and $1,000 at maturity. Suppose the price for this bond is$1,000.

A. Calculate the interest (yield to maturity) for this bond. You need to write the equa- tion to show how to calculate.

B. Now suppose the Fed intervene the bond market through open market operation to raise the bond price to $1,100. Please calculate the interest (yield to maturity) for this bond. You need to write the equation to show how to calculate.

C. Now suppose the Fed intervene the bond market through open market operation to lower the bond price to $900. Please calculate the interest (yield to maturity) for this bond. You need to write the equation to show how to calculate.

D. Now, we can study the relationship between bond prices and interest rates. From previous two questions, we can conclude that the bond price is (positively, negatively) correlated to the interest.

Answer 1

The formula for yield to maturity YTM is

Here C is coupon payment, F is face value, P is price and n is no. of years.

A.

Here C i$100, F is $1000, P is $1000 and n is 5 years. Now YTM is

=(100+(1000-1000)/5) / (1000+1000)/2

=100/1000

=0.1=10%

B.

Here C i$100, F is $1000, P is $1100 and n is 5 years. Now YTM is

=(100+(1000-1100)/5) / (1000+1100)/2

=80/1050

=0.0762=7.62%

C.

Here C i$100, F is $1000, P is $900 and n is 5 years. Now YTM is

=(100+(1000-900)/5) / (1000+900)/2

=120/950

=0.1263=12.63%

D.

From the above three scenarios we can see that as bond price increase, interest rate or YTM decreases and vice-versa, so it can be said that bond price is negatively correlated to the interest.