Question

A $100 bond with 4% coupon rate matures in 25 years. It bears semiannual coupons and is purchased for $117.50 to yield i(2). A $100 bond with 5% coupon rate also matures in 25 years. It also bears semiannual coupons, but is purchased for $135.00 to yield i(2). What is i(2)?

Answer 1

4. At least 2.75%, but less than 3.25%

Step-by-step explanation:

missing options:

1. Less than 1.75%
2. At least 1.75%, but less than 2.25%
3. At least 2.25%, but less than 2.75%
4. At least 2.75%, but less than 3.25%
5. 3.25% or more

i⁽²⁾ = approximate YTM = {2 + [(100 - 117.50)/50]} / [(100 + 117.50)/2] = 1.65 / 108.75 = 1.517% x 2, annual rate = 3.03%

i⁽²⁾ = approximate YTM = {2.50 + [(100 - 135)/50]} / [(100 + 135)/2] = 1.80 / 117.50 = 1.532% x 2, annual rate = 3.06%

Since both YTMs are very similar, we can determine that i⁽²⁾ is approximately 3%, maybe a little less or a little more, since we are using the approximate yield to maturity formula.