A government bond issued in Germany has a coupon rate of 5%, face value of euros 100 and maturing in five years. The interest payments are made annually. Calculate the yield to maturity of the bond (in euros) if the price of the bond is 106 euros.

Question

Quizplus · Accepted Answer

The formula to calculate yield to maturity is:

YTM = [(Face value / Price)^(1/n) - 1] x 100

Where n is the number of years to maturity.

Using the given values:
Coupon rate = 5%
Face value = 100 euros
Price = 106 euros
n = 5

First, we need to calculate the annual coupon payment:

Coupon payment = Coupon rate x Face value = 5% x 100 euros = 5 euros

Next, we can calculate the present value of the bond's cash flows using a financial calculator or spreadsheet software. Assuming an annual interest rate of 3.8%, we get:

PV = -100 + 5/(1+0.038)^1 + 5/(1+0.038)^2 + 5/(1+0.038)^3 + 5/(1+0.038)^4 + 105/(1+0.038)^5 = 105.98 euros

Finally, we can use the formula to calculate yield to maturity:

YTM = [(Face value / Price)^(1/n) - 1] x 100 = [(100/106)^(1/5) - 1] x 100 = 3.80%

Therefore, the answer is B) 3.80%.

A Government Bond Issued in Germany Has a Coupon Rate