Suppose the spot price of gold is \$300 per ounce and the risk-free interest rate for one year is 5%. What is a reasonable value for the one-year forward price of gold?
The answer is \$315, right?
Suppose the one-year forward price of gold is \$340. Argue as follows: borrow 300 dollars for a year and buy one ounce of gold. Then short a forward contract to sell the gold in one year time. Show this will lead to a risk-free profit (arbitrage) and the the one-year forward price of gold must be $315.
This comes down to \$340 - $315 = \$25 , right?
I suppose that the \$315 here cones again from the \$300*105% ? right?
Then assume the one-year forward price of gold is \$300. Argue as follows: sell the gold, then invest the proceeds and long a one-year forward on gold. Show again that this will lead to a risk-free profit (arbitrage) and the one-year forward price of gold must be \$315.
I'm confused cause of this part. So if anybody could help?
thanks in advance
I don't know what goes wrong with the notation but when I design the question I don't have a problem until I upload the text. Therefor I wanted to upload an image. enter image description here
Your first part is correct.
For the second part, if the forward price of gold is the same as the spot price then you can sell the gold today for $\$300$ and put the money into an account earning $5\%$ interest. At the same time you go long on a one year forward contract. This means you agree to pay $\$300$ an ounce a year from now.
In a year you have $\$315$ from the return on your investment so you can buy your gold back and earn a free $\$15$. That's what arbitrage is. Since everyone would do this it would drive the forward price up to $\$315$.