Calculate the futures price of a 3-month futures contract on the share of Lansdowne Ltd when the price is R80, and the risk-free rate is 7%.Select one:a.R80.00b.R81.36c.R85.60d.R82.75
Question
Calculate the futures price of a 3-month futures contract on the share of Lansdowne Ltd when the price is R80, and the risk-free rate is 7%.Select one:a.R80.00b.R81.36c.R85.60d.R82.75
Solution
The futures price (F) of a financial asset can be calculated using the formula:
F = S * e^(r*t)
where: S = the spot price of the asset r = the risk-free interest rate t = the time to delivery (in years)
In this case, S = R80, r = 7% or 0.07 (you need to convert the percentage into a decimal), and t = 3/12 = 0.25 (since 3 months is a quarter of a year).
Substituting these values into the formula gives:
F = 80 * e^(0.07*0.25)
Using the value of e (approximately 2.71828), the calculation becomes:
F = 80 * 2.71828^(0.07*0.25)
Solving this gives:
F = R81.36
So, the futures price of a 3-month futures contract on the share of Lansdowne Ltd when the price is R80, and the risk-free rate is 7% is R81.36. Therefore, the correct answer is b. R81.36.
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