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.

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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