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The spot price of silver is now $9 per ounce. The storage costs for silver are $0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, what is the futures price of silver for delivery in nine months?A. $9.1756 B. $9.8902 C. $10.5418 D. $8.8797

Question

The spot price of silver is now 9perounce.Thestoragecostsforsilverare9 per ounce. The storage costs for silver are 0.24 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, what is the futures price of silver for delivery in nine months?A. 9.1756B.9.1756 B. 9.8902 C. 10.5418D.10.5418 D. 8.8797

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Solution

The futures price of a commodity like silver can be calculated using the formula:

F = S * e^(r + s)t

where: F = futures price S = spot price r = risk-free interest rate (annual) s = storage cost (annual, as a proportion of the spot price) t = time to delivery (in years)

Given in the problem: S = 9r=10s=9 r = 10% = 0.10 s = 0.24/$9 = 0.02667 (approx) t = 9/12 = 0.75 years

Substituting these values into the formula:

F = 9 * e^(0.10 + 0.02667) * 0.75

Calculating the exponent first:

0.10 + 0.02667 = 0.12667 0.12667 * 0.75 = 0.095

So:

F = 9 * e^0.095

Using the value of e (approximately 2.71828):

F = 9 * 2.71828^0.095

Calculating the exponent:

2.71828^0.095 = 1.099 (approx)

So:

F = 9 * 1.099 = $9.89 (approx)

So, the futures price of silver for delivery in nine months, given the provided spot price, storage costs, and interest rates, is approximately 9.89.Therefore,theclosestanswerisB.9.89. Therefore, the closest answer is B. 9.8902.

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