For an equity index (the Nifty 50, the S&P 500) the carry benefit is the dividend stream the index pays out, expressed as a continuous yield q (a clean simplification for a broad, frequently-rebalanced basket). The fair forward/futures price is:
F0 = S0 × e^{(r − q)T}
Read the sign: dividends are a benefit of holding the underlying that the forward-holder does not receive (you hold a claim on the index's future price only, not its dividends), so the financing cost is reduced by q. If r > q (the usual case), the future trades above spot, a state called contango; if q > r (rare for equity indices, common for high-yield single stocks), the future can trade below spot. Worked Example 1 prices a live-style Nifty future this way, checks it against a quoted price, and sizes the resulting arbitrage; Worked Example 3 repeats the exercise for the CME E-mini S&P 500 and, additionally, inverts the formula to back out the market's implied financing rate from a quoted price, a genuinely useful skill, because it tells you what repo rate the futures market is pricing in without your ever having observed that rate directly.
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How do you price a single-stock forward?
A single stock forward, an OTC contract, common for a block-deal hedge or an executive's concentrated-position unwind (PW1.01's territory) rather than an exchange product, is usually priced off discrete, dated cash dividends rather than a smooth continuous yield, because a single company pays two or four dividends a year on known dates, not a continuous drip. The method is to net the present value of those specific dividends out of today's spot price before compounding the rest forward:
F0 = (S0 − PV(dividends)) × e^{rT}
This is not a different theory, it is the same replicating-portfolio argument, just with the carry benefit computed as a discrete cash amount at a known date instead of a smoothed annual rate. Practice problem P16 walks this through end to end on a synthetic Indian stock, and, instructively, shows how much a forward is overstated if you forget the dividends entirely.
Do futures and forwards have the same price?
One nuance worth flagging even though it rarely bites at the maturities this module works with: theoretically, a futures price and a forward price on the same underlying, same maturity, are identical only if interest rates are deterministic (or, more precisely, uncorrelated with the underlying). Daily marking-to-market means a futures long earns interest on daily gains and pays interest on daily losses; if the underlying is positively correlated with interest rates, that daily resettlement systematically favors the long futures position (gains arrive when reinvestment rates are high), so the futures price runs slightly above the theoretical forward price to compensate, and slightly below it if the correlation is negative. For the equity-index and short-dated FX and commodity examples in this module the effect is a rounding error and we ignore it (as does almost every practitioner at these tenors); it becomes material only for long-dated contracts on assets tightly correlated with rates, the reason Eurodollar/SOFR futures carry a well-known convexity adjustment in professional curve-building, which is FI1.03's territory, not this module's.