In this workout, we are asked to calculate first, a fair equity forward price, and secondly, a fair equity index futures price. For the equity forward contract we're given the cash price of $45 per share. That is the cost of buying the underlying stock in the market today, interest rates of 2%, the dividend per share to be paid over the course of the forward period of 50 cents and a delivery date of one year. To calculate the fair forward price, we first of all need to take the cash price. This is the money we would have to spend if we were going to buy the underlying asset in the market today. We then need to deduct from this the dividends per share. This is a benefit that we will not be receiving if we enter into a contract today to buy this underlying stock in one year's time, as the dividend will be paid before we buy the shares in one year's time. So therefore, we won't be entitled to those dividends through this forward contract. We also need to add on to this the interest cost which is the interest rate of 2% multiplied by the cash price. This is the interest we would incur if we were to borrow $45 to buy the stock today. Taking all of those together gives us a fair forward price of $45.40. This is the net cost we will incur if we buy the underlying stock today and hold it for a year, meaning that we own the stock in one year's time. We would've had to pay the interest on the cash borrow to buy the stock and we would have received the dividend offsetting some of that cost. As such, this is also the arbitrage free, fair forward price. Moving down to the index future for this equity index future around the S&P 500 index, all of the calculations take place in index points. The future's contract will specify the dollar value of one index point, so all of the calculations are in index points, so we would need to take the index points value today. We would then need to deduct from that any dividends on the index. However, since the dividends are not specifically stated on the underlying index, but rather the dividends are earned on an ongoing basis, it is more common to express the dividends as a dividend yield rate. However, because this future's contract expires only in six months' time, delivery date here is expressed as 0.5 of a year. We only need to strip out of this half a year's worth of dividends, so we need to take the dividend yield rates, multiply it by the index value, and multiply it by the time until the delivery date on the forward contract. The calculation here is based on discreet discounting. It is also possible to use continuous compounding here, but for simplicity in this workout we've used discrete compounding. We then need to add on the interest cost where the interest rate 1.5%. Multiply this by the index points, and again, by the time until the delivery of the contract, half a year or six months. The result here is that the fair futures price is lower than the cash price. However, this is only because the dividend yield. The benefits of owning the underlying stock is greater than the cost of owning the underlying stock. The interest rate of 1.5%.