This is an IELTS formal letter example.
It is formal as it is to an insurance company, and is not to someone that you know. It is an example of how to write a letter of complaint.
See comments on the letter at the bottom of the page.
The answer clearly addresses all the bullet points from the question. The writer gives reasons why the letter is being written and why the increase is considered unfair, and then goes on to explain what he wants the company to do to resolve the situation.
The writer expands on his ideas by giving extra details. For example, he explains that he has had insurance for seven years and never had an accident, and he also explains how the increase will affect him i.e. result in a 20% rise in his payments. It is important when writing a letter to give extra information to support the letter whilst remaining on topic.
The tone of the IELTS formal letter is well-controlled, with appropriate opening (Dear Sir / Madam) and closing (Yours faithfully) phrases, and further phrases that ensure the formal letter still remains polite (I understand that..., I’m afraid..., I look forward to hearing from you...) despite the fact that it is a letter of complaint.
There are some other good examples of phrases appropriate to a semi-formal or formal letter (As you will be aware..., I would therefore like you to...).
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