Question

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 (continuous compounding) for all maturities, calculate the futures price of silver for delivery in nine months.

a) $24.75
b) $24.95
c) $25.15
d) $25.35

Answer 1

The futures price of silver for delivery in nine months is $24.95. Option b is correct.

Step-by-step explanation:

To calculate the futures price of silver for delivery in nine months, we need to consider the spot price of silver, storage costs, and the interest rate. The formula for calculating the futures price is:

Futures Price = Spot Price + Storage Costs - Present Value of Storage Costs

Using the given information, the storage costs per ounce per year are $0.24 and are payable quarterly in advance. The interest rate is 5% per annum with continuous compounding. We need to calculate the present value of the storage costs for nine months.

Plugging in the values into the formula, we get:
Futures Price = $25 + ($0.24 * 9/12) - ($0.24 * (1 - e^-0.05 * 9/12))

Calculating the expression, we find that the futures price of silver for delivery in nine months is $24.95.