Question

The spot price of silver is $20 per ounce. The storage costs are $0.30 per ounce per year payable quarterly in advance. Assuming that interest rates are 4% per annum for all maturities, calculate the futures price of silver for delivery in 12 months.

Answer 1

21.11176754

Step-by-step explanation:

storate cost: 0.30

as the storage is continusly we use continuos interest rate:

0.30 / 4 = 0.075 per quarter

this is paid in advance so we calculate the present values of this payment

`PV = 0.075 + 0.075e^(-0.04 * 0.25) + 0.075e^(-0.04 * 0.50)+0.075e^(-0.04 * 0.75)`

PV = 0.295552053

Now we solve for the future value of silver using also a continuos rate

`F = (spot + storage) e^(0.04 * 1)`

(20 + 0.295552053)e^0.04 = 21.11176754