Let's have a look at some simple examples on how to calculate futures prices. The spot price of soybeans is $921. The standard contract is 5,000 bushels, and the storage cost for the time period is 2 cents per bushel. The risk-free rate is half a percent. What does a six months futures contract on soybeans cost? Well, the first thing we're going to calculate is the spot price, including storage costs. So we start with the spot price plus the storage cost per bushel, times the number of bushels. The risk-free rate is half a percent and the time period needs to be expressed in years. So that's six months divided by 12 i e half a year. We've been given Eulers number in the example. So we can now calculate the future's price.

Spot price, including storage costs times Euler's number to the power of the risk-free rate of half a percent compounding continuously for a time period of half a year. Close the bracket, hit enter. The futures price is 1023.6. A slightly simpler way to do this is to use an Excel function to help us. So we're simply gonna start with a spot price, including storage costs times X, which is a reflection of we're now using Euler's number and we're going to use that for a time period of half a year. Compounding the risk-free rate of 0.5%, close the bracket, hit enter, and we get exactly the same futures price. Now what happens when spot prices move? Well, let's look at part B of this question one month later, the spot prices of soybeans is $910, so it's dropped a little bit. The risk for rate and the storage costs remain the same. So we've simplified this slightly in that storage cost for five months are the same as the previous six months. The buyer of the six months futures contract in the previous workout must mark his contract to market. So he must figure out whether he made money or lost money here. So let's figure out first of all, the spot price, including storage costs. That's gonna be the spot price plus storage cost per bushel times the number of bushels again. The risk-free rate of course, remains 0.5% per annum, but the period has now changed. There's only five months left, of course, making for 0.4 of a year. We have Euler's number there again, so we can figure out the future's price. Now, after one month. Spot price including storage costs times Euler's number to the power of half a percent times the remaining time to maturity, 0.4 years, close the bracket, hit enter. So the futures price is now 1012.1. So did he make money or did he lose money? Well, it's 1012.1 now, and it used to be 1023.6. So the buyer of this contract has just lost $11.40.