What is the relationship between the interest rate and the call or put options?

This is an interesting question. The best way to see it is to understand the fundamental of finance, namely, money has price! If you encounter questions like this in the exam, you want to know how much you have to “pay” and how much is the “gain”.

If you expect a stock to grow, you have two choices. One is to buy the stock at full price while another one is to buy call options. You can leverage the investment by borrowing money to buy stocks, or as for call option, it requires less capital (so it is a leverage already by itself) but you have to pay the extra premium. Therefore, if the interest rate increases, it means the cost of capital is getting higher. The extra premium you paid for stock options might offset the interest cost. Therefore, you prefer buying more stock options than the stock asset itself. So, the demand for call options will increase and thus the option price will increase also.

How about for put options? The answer is opposite. As the interest rate increases, the put option price decreases. Why? The explanation will be posted later.