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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

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    $\begingroup$ The notation went funny because dollar signs are used here to delimit "math mode" based on LaTeX. In order to have a dollar sign show up, put a backslash in front of it. (I've edited this fix into your post - it should show up soon) $\endgroup$ – jmerry Jan 4 at 4:26
  • $\begingroup$ Waw, that really is an eye-opener to me! Thanks for helping me out! As you might have figured. I'm new to this website. $\endgroup$ – Nicolas Cloet Jan 4 at 6:22
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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 $\$315$.

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