Question

a 10-year, 8% coupon bond currently sells for $90. a 10-year, 4% coupon bond currently sells for $80. what is the 10-year zero rate?

Answer 1

The 10-year zero rate can be calculated by comparing the prices of the two bonds using the formula ((1 + Coupon / Face Value) ^ (1 / Years) - 1) * 100. For the 8% coupon bond, the zero rate is 7.18%, and for the 4% coupon bond, the zero rate is 3.96%. Therefore, the 10-year zero rate is approximately 7.18%.

Step-by-step explanation:

The 10-year zero rate can be calculated by comparing the prices of the two bonds. In this case, the 8% coupon bond is priced at $90 and the 4% coupon bond is priced at $80. Using the formula:

Zero rate = ((1 + Coupon / Face Value) ^ (1 / Years) - 1) * 100

For the 8% coupon bond:

Zero rate = ((1 + 0.08 / 1000) ^ (1 / 10) - 1) * 100 = 7.18%

And for the 4% coupon bond:

Zero rate = ((1 + 0.04 / 1000) ^ (1 / 10) - 1) * 100 = 3.96%

Therefore, the 10-year zero rate is approximately 7.18%.