34) if a security pays $110 next year and $121 the year after that, what is its yield to maturity if it sells for $200? a) 9 percent b) 10 percent c) 11 percent d) 12 percent

The answer is B, 10%.

Explanation:

200 = (1 + i) 110

(1 + i)

2 +

121

(1 + i)

2

200 = (110 + 110i) + 121

(1 + i)

2

200 (1 + i)

2 = 110 + 110i + 121

200 ¡

1+2i + i

2

¢

= 231 + 110i

200 + 400i + 200i

2 = 231 + 110i

200i

2 + 290i − 31 = 0 (3)

From here, using the formula for the solution of a general quadratic equation,

ax2 + bx + c = 0 (4)

one can obtain

x1,2 = −b ± √b2 − 4ac

2a (5)

and thus

i1,2 = −290 ± p2902 − 4 × 200 × (−31)

2 × 200

The interest rate is bounded to be positive, by definition, so we would consider only the

positive of the two roots,

i = −290 + p2902 − 4 × 200 × (−31)

2 × 200

2

i = −290 + √84100 + 24800

400

i = −290 + √108900

400

i = −290 + 330

400

i = 40

400 = 1

10 = 0.1, i.e., 10%.