The statement that the forward price will fall if interest rates rise is inaccurate. In fact, the opposite is true. The forward price of a contract is directly influenced by the level of interest rates. When interest rates increase, the cost of carrying the underlying asset until the delivery date also increases. This cost is reflected in the forward price. Therefore, when interest rates rise, the forward price also rises. This relationship is captured in the forward price formula:

$F = (S - I)(1 + R)^T$

where $F$ is the forward price, $S$ is the spot price of the underlying asset, $I$ is the income from the asset (such as dividends), $R$ is the risk-free interest rate, and $T$ is the time to maturity. As shown by the formula, the forward price $F$ is directly proportional to the interest rate $R$. Therefore, an increase in $R$ leads to an increase in $F$, not a decrease as the statement suggests.

Choice B is incorrect. The forward price is indeed directly linked to the level of the stock market index. This is because the forward price is determined by the spot price of the underlying asset, which in this case is the S&P 500 index. Therefore, changes in this index will directly affect the forward price.

Choice C is incorrect. If we increase the time to maturity while keeping all other factors constant, it would indeed lead to an increase in forward prices. This happens due to the cost-of-carry model where longer time periods allow for more accumulation of interest costs, which are factored into pricing a forward contract.

Choice D is incorrect. If dividend payments on underlying stocks increase, it would actually cause a decrease in forward prices. This happens because higher dividends reduce expected future spot prices (as some value has been paid out as dividends), and hence lower future spot prices lead to lower forward prices.