The 1 year spot rate is 2.5%. The YTM of a bond due in 2 years is 3.7%. The bond pays 3% coupon annually. The 2-year spot rate is

Based on the given YTM of a bond, the 1 year spot rate, and the bond payment, the 2-year spot rate is 3.72%.

What is the 2-year spot rate?

First find the coupon payment:

= 3% x 1,000 face value

= $30

The 2 year spot rate can be found in the formula:

(Coupon payment / (1 + YTM)) + ( (Face value + Coupon) / (1 + YTM)²) = (Coupon payment / (1 + 1 year spot rate)) + ( (Face value + Coupon) / (1 + 2-year spot rate)²)

Solving gives:

30/1.037 + 1,030/1.037² = 30/1.025 + 1,030/(1 + 2 year spot rate)²

986.74 = 29.268 + 1,030/(1 + 2 year spot rate)²

957.472 = 1,030/(1 + 2 year spot rate)²

(1 + 2 year spot rate)² = 1,030 / 957.472

2 year spot rate = 1.037183 - 1

= 3.72%

In conclusion, the 2-year spot rate is 3.72%.

Find out more on spot rates at .