The spot rate on a non-dividend-paying stock is $15.70. The risk-free rate is 3.15% and the market rate is 10.75%. What is the 3-month futures rate if spot-futures parity exists?
A)$15.48
B)$15.82
C)$16.01
D)$16.13
E)$16.24

Question

Quizplus · Accepted Answer

According to spot-futures parity:
F = S(1 + r - q)^t
where F is the futures price, S is the spot price, r is the risk-free rate, q is the dividend yield, and t is the time to expiration (in years).
Since the stock is non-dividend paying, q = 0.
The time to expiration is 3 months or 0.25 years.
Thus,
F = $15.70(1 + 0.0315 - 0)^0.25
F = $15.82
Therefore, the 3-month futures rate is $15.82. The answer is B.

The Spot Rate on a Non-Dividend-Paying Stock Is $15