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13 September, 08:34

The spot price of silver is $25 per ounce. The storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 5% per annum for all maturities, calculate the futures price of silver for delivery in 9 months.

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  1. 13 September, 09:31
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    The future price of Silver is $26.14

    Explanation:

    First we compute Total storage costs (Tsc) in the future given by the equation:

    Tsc = (Sc/4) * [ 1 + exp (-rT1) + exp (-rT2) ]

    where Sc is the storage cost today

    where r is the rate

    Sc = $0.24

    T1 = 3/12

    T2 = 6/12

    r = 5%=5/100

    = 0.05

    Tsc = (0.24/4) [ 1 + exp (0.05*3/12) + exp (0.05*6/12) ]

    Tsc = 0.06 [ 1 + exp (-0.05*0.25) + exp (-0.05*0.5) ]

    Tsc = 0.178

    The future price (Fv) is given by:

    Fv = (Sp + Tsc) * exp (rt)

    where Sp is the spot price of silver

    where r is the interest rate

    where t is the delivery time ratio (9 months compared to 12 months)

    Sp = $25

    r = 5%

    = 5/100=0.05

    t = 9/12

    =0.75

    Fv = (25. 000+0. 178) * e xp (0. 05*0.75)

    Fv = $26. 14
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