The question is based on the concept of put-call parity, which is a relationship between the prices of European put and call options with the same strike price and expiration date. The equation for put-call parity in this context is:

$c = S_0 + p - PV(K) - PV(D)$

Where:

• $c$ is the call price (to be determined),
• $p$ is the put price (USD 3.00),
• $S_0$ is the current stock price (USD 26.00),
• $K$ is the strike price of the put option (USD 25.00),
• $PV(K)$ is the present value of the strike price,
• $PV(D)$ is the present value of the dividend,
• $t$ is the time to the next dividend (0.25 years).

The present value of the strike price $PV(K)$ is calculated using the formula $PV(K) = K * e^{-rt}$, where $r$ is the continuously compounded risk-free rate (5% per year) and $t$ is the time to maturity (0.5 years for the option and 0.25 years until the dividend). Thus, $PV(K) = 25.00 * e^{-0.05*0.5} = 24.3827$.

The present value of the dividend $PV(D)$ is calculated similarly, $PV(D) = D * e^{-rt}$, where $D$ is the dividend amount (USD 1.00) and $t$ is the time until the dividend is paid (0.25 years). Thus, $PV(D) = 1.00 * e^{-0.05*0.25} = 0.9876$.

Plugging these values into the put-call parity equation gives:

$c = 26.00 + 3.00 - 24.3827 - 0.9876 = 3.6297$

This result, rounded to two decimal places, is USD 3.63, which corresponds to option C. The other options are incorrect due to various misinterpretations of the put-call parity formula or the values involved:

• Option A (USD 2.37) would be the value of the put option if the question mistakenly switched the call and put prices.
• Option B (USD 3.01) would be the result if the strike price itself, rather than its present value, were used in the formula.
• Option D (USD 4.62) would be the value if the dividend payment were ignored.

The correct answer is C, USD 3.63, which is closest to the calculated value of the call option using the put-call parity relationship and the given financial data.