To price a European call option using the binomial model:

1. Calculate the risk-neutral probability: $p = \frac{e^{rT} - d}{u - d}$ Where:

   • u = 13/10 = 1.3
   • d = 7/10 = 0.7
   • r = 4% = 0.04
   • T = 0.25

   $e^{rT} = e^{0.04 \times 0.25} = e^{0.01} ≈ 1.01005$ $p = \frac{1.01005 - 0.7}{1.3 - 0.7} = \frac{0.31005}{0.6} ≈ 0.51675$

2. Calculate the option payoffs:

   • If stock price = $13: payoff = max(13 - 10, 0) = $3
   • If stock price = $7: payoff = max(7 - 10, 0) = $0

3. Calculate the expected payoff: $Expected\ payoff = p \times 3 + (1-p) \times 0 = 0.51675 \times 3 = 1.55025$

4. Discount to present value: $Option\ price = e^{-rT} \times Expected\ payoff = e^{-0.01} \times 1.55025 ≈ 0.99005 \times 1.55025 ≈ 1.535$

However, this calculation gives approximately $1.535, which doesn't match option A ($0.97). Let me recalculate more carefully:

$p = \frac{1.01005 - 0.7}{1.3 - 0.7} = \frac{0.31005}{0.6} = 0.51675$ $Expected\ payoff = 0.51675 \times 3 = 1.55025$ $Discount\ factor = e^{-0.01} = 0.99005$ $Option\ price = 1.55025 \times 0.99005 = 1.5347$