Question

Jordan bought a 4% semi-annual coupon bond with 25 years to maturity at par value of

$1,000. If the required rate of return (yield to maturity )of this bond increases to 4.25%, by
how much does the value of the bond change?
A) minus $38.04
B) plus $39.28
C) minus $38.27
D) The value does not change if Jordan intends to hold the bond to maturity.

Answer 1

The change in the value of the bond is minus $38.27. The correct answer is option C) minus $38.27.

Step-by-step explanation:

We can use the formula for the present value of a bond:

Bond Value = (Coupon Payment / (1 + Yield)^Frequency) + (Coupon Payment / (1 + Yield)^(2 * Frequency)) + ... + (Coupon Payment + Par Value / (1 + Yield)^(n * Frequency))

Here, the bond has a semi-annual coupon payment (Frequency = 2) and a 25-year time to maturity (n = 25).

First calculate the initial bond value, assuming a yield to maturity of 4%:

Bond Value_initial = (40 / (1 + 0.04)^1) + (40 / (1 + 0.04)^2) + ... + (40 + 1000 / (1 + 0.04)^(25 * 2))

After simplifying and calculating the above expression, we find:

Bond Value_initial = $1000

Now, calculate the bond value when the yield to maturity increases to 4.25%:

Bond Value_final = (40 / (1 + 0.0425)^1) + (40 / (1 + 0.0425)^2) + ... + (40 + 1000 / (1 + 0.0425)^(25 * 2))

After evaluating the expression, we find:

Bond Value_final = $961.73

To find the change in the bond value, we subtract the final bond value from the initial bond value:

Change in Bond Value = Bond Value_final - Bond Value_initial

= $961.73 - $1000

= -$38.27

Thus, The correct Option is C.