Final answer:
The forward price of gold for delivery in 9 months can be calculated by adding the storage costs to the current price and adjusting for the time value of money using the continuously compounded risk free rate.
Step-by-step explanation:
The forward price of 1 ounce of gold for delivery in 9 months, considering a current price of $30 per ounce, storage costs of $0.12 per ounce per quarter payable in advance, and a continuously compounded risk free rate of 2.66%, is calculated using the cost of carry model. We must account for the current price, the cost of storing the gold, and the time value of money due to the risk free rate to compute this price.
First, determine the total storage cost for 9 months (3 quarters) which would be $0.12 * 3 = $0.36. Next, calculate the continuous compounding factor with the formula ert, where e is the base of the natural logarithm, r is the risk free rate, and t is the time in years (0.75 years for 9 months). The forward price is then computed as (Spot Price + Storage Costs) * ert, which becomes ($30 + $0.36) * e(0.0266)(0.75).