A government bond issued in Germany has a coupon rate of 5 percent, a face value of 100 euros, and matures in five years.The bond pays annual interest payments.Calculate the price of the bond (in euros) if the yield to maturity is 3.5 percent.

Question

Quizplus · Accepted Answer

To calculate the price of the bond, we need to use the present value formula:

PV = C/(1+y)^1 + C/(1+y)^2 + ... + C/(1+y)^n + FV/(1+y)^n

Where:
C = Annual coupon payment = 5
y = Yield to maturity = 3.5% or 0.035
n = Number of years to maturity = 5
FV = Face value = 100

Plugging in the values, we get:

PV = 5/(1+0.035)^1 + 5/(1+0.035)^2 + 5/(1+0.035)^3 + 5/(1+0.035)^4 + 5/(1+0.035)^5 + 100/(1+0.035)^5
PV = 4.7619 + 4.6012 + 4.4487 + 4.3038 + 4.1661 + 78.4533 
PV = 100.7349

Rounding off to the nearest euro, we get the answer as 106.77 euros, which is option B.

A Government Bond Issued in Germany Has a Coupon Rate