Introduction:
The cheapest mode of communication is a letter.

Explanation:
- Mobile phone: While mobile phones have become a widely used mode of communication, they are not the cheapest option. Mobile phone services usually require a subscription or a prepaid plan, which involves costs for voice calls, SMS, and data usage. Therefore, mobile phones are not the cheapest mode of communication.

- Email: Email is a digital mode of communication that allows users to send messages electronically. While email services are generally free to use, they do require access to the internet, which can incur costs. Additionally, email services may require devices such as computers, laptops, or smartphones, which have their own associated costs. Therefore, email cannot be considered the cheapest mode of communication.

- SMS: SMS (Short Message Service) is a text messaging service available on mobile phones. While SMS messages are generally cheaper than voice calls, they still require a mobile phone with a subscription or a prepaid plan. Therefore, SMS cannot be considered the cheapest mode of communication.

- Letter: A letter is a physical form of communication that involves writing a message on paper, putting it in an envelope, adding a stamp, and mailing it through postal services. Letters are generally considered the cheapest mode of communication because they do not require any subscription or ongoing costs. The only expense involved is the cost of paper, envelope, and stamp. Compared to electronic modes of communication, letters can have a longer delivery time, but they are still a cost-effective option for certain situations.

Conclusion:
Considering the available options, a letter is the cheapest mode of communication as it does not require any subscription or ongoing costs, unlike mobile phones, email, or SMS.