The question is related to the valuation of American-style call and put options using the put-call parity principle. The put-call parity is a fundamental relationship in options pricing that states that the price of a call option should be equivalent to the price of a put option plus the present value of the difference between the exercise price and the current stock price.

Given the scenario:

• American-style call and put options with 3 months to maturity.
• Non-dividend-paying stock at USD 40.
• Strike price for both options at USD 35.
• Risk-free rate at 1.5%.

The put-call parity for American options can be expressed as an inequality: $So - Ke^{-rT} \leq C - P \leq So - K$

Where:

• $C$ is the price of the call option.
• $P$ is the price of the put option.
• $So$ is the current stock price.
• $K$ is the strike price.
• $r$ is the risk-free rate.
• $T$ is the time to maturity.

Plugging in the given values:

• $So = 40$
• $K = 35$
• $r = 0.015$ (1.5% as a decimal)
• $T = \frac{3}{12}$ (3 months as a fraction of a year)

The lower bound of the difference $(C - P)$ is straightforward: $40 - 35 = 5$

For the upper bound, we calculate the present value factor: $e^{-0.015 \times \frac{3}{12}} \approx 0.995$

So the upper bound is: $40 - 35 \times 0.995 \approx 5.13$

Thus, the bounds on the difference between the prices of the call and put options are: $5 \leq C - P \leq 5.13$

The correct answer is B, which states that the lower bound is 5.00 USD and the upper bound is 5.13 USD. This is consistent with the put-call parity for American options and the given parameters.