The spot price of oil is $50 per barrel and the cost of storing a barrel of oil for one year is $3, payable at the end of the year. The risk-free (continuously compounded) interest rate is 5% per annum, continuously compounded. What is an upper bound for the one-year futures price of oil?

$55.56

Explanation:

Given the following ;

Spot price per barrel = $50

Storage cost = $3 per barrel

Interest rate(i) = 5% (continously compounded)

Period (t) = 1

Upper bound future price.

Upper bound future price = spot price per barrel + storage cost

Storage cost per barrel = $3, compounded at 5 % per annum for one year.

5÷100 = 0.05

Mathematically, present value of storage cost per barrel =

3e^-(i × t) = 3e^-(0.05×1)

3e^-(0.05) = 2.854

Upper bound for one year future price

($50+$2.854)e^0.05×1

52.854e^0.05 = $55.56

the first one $24,630

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