The relationship between futures price, spot price, storage costs, risk-free rate, and convenience yield is:

$F = (S + U) \left[ \frac{1 + R}{1 + Y} \right]^T$

where:

• F = futures price
• S = spot price
• U = present value of the storage cost
• R = risk-free rate
• Y = convenience yield
• T = time to maturity of futures contract

We can rewrite the above equation so that:

$Y = \left[ \frac{S + U}{F} \right]^{\frac{1}{T}} (1 + R) - 1$

$= \left[ \frac{95 + 10}{100} \right]^{\frac{1}{0.5}} (1.05) - 1$

$= \left[ \frac{105}{100} \right]^{2} (1.05) - 1$

$= (1.05)^2 (1.05) - 1$

$= 1.157625 - 1$

$= 0.157625$

That is, the convenience yield is approximately 15.8%.