Cash Equitization

This is from Level 3 Derivatives Textbook Page 326
Cash Equitization
Georgia McMillian manages a fund invested in UK stocks that is indexed to the FTSE 100 Index. The fund has £250 million of total assets under management, including £20 million of cash reserves invested at the three- month British pound floating rate of 0.63% (annualized). McMillian does not have an expectation on the direction of UK stocks over the next quarter. However, she is keen to minimize tracking error risk, so she implements a cash equitization strategy attempting to replicate the performance of the FTSE 100 on the cash reserves. Futures on the FTSE 100 settling in three months currently trade at a price of £7,900, the contract’s value is £10 per index point (so each futures contract is worth £79,000), and its beta, βf, is 1.0.
McMillian engages in a synthetic index strategy to gain exposure on a notional amount of £20 million to the FTSE 100 by purchasing equity index futures. The number of futures she must purchase is given by the following:
Nf = (βT/βf) * (S/F) = (1.0/1.0) * (20000000/79000) = 253.16
where the beta of the futures contract, βf, and the target beta, βT, are both equal to 1.0.

Scenario: Three months later, the FTSE 100 Index has increased by 5%.
Three months later, the FTSE 100 has increased by 5%, and the original value of £230 million invested in UK stocks has increased to £241.5 million. The price of the FTSE 100 Index futures contract has increased to £8,282.5. Interest on the cash invested at the three- month floating rate amounts to £31,500 (£20,000,000 × 0.63% × 90/360).
McMillian bought the futures at £7,900, and the cash settlement of the contract at is £8,282.5. So, there is a “gain” of 382.5 index points, each point being worth £10, on 253 contracts for a total cash inflow of £967,725 (382.5 points per contract × £10 per point × 253 contracts). Adding to the portfolio the profit from the futures and the cash reserves plus the interest earned on the cash gives a total market value for McMillian’s portfolio of £262,499,225 (= £241,500,000 + £20,000,000 + £967,725 + £31,500). The rate of return for the combined position is: £262,499,225/£250000000 - 1 = 5%

Hi, I don’t understand why £31,500 should be included in the calculation of total market value. Georgia used 20 million to buy equity index futures and he lost the opportunity to invest 20 million in the 3-month floating rate.
Could you give me a hint about my question?

When you buy a futures contract, you don’t pay the purchase price upfront, just a margin. Here, they invested cash that will be used to buy futures.

Thank you.
One more question, are the margins of futures contract be ignored here?

Depends what the question says but if silent then yes given they’re usually a fraction of the futures contract