Hi,
This is not a request that would be normal in Canada, but I assume that it is fine in your country.
I have simply corrected your English.
1 Subject: Personal loan
Dear Sir,
This is in reference to the above subject.
One of our staff members, Mr. X, has requested a personal loan in the amount of $ ***.*** for his vacation expenditure.
He is willing to pay it back, within six months, from his monthly salary.
(You haven't said what you want the recipient of this letter to do. Do you want their approval?)
Thanking you in anticipation.
2 Subject: Personal loan
Dear Mr.X,
As I am planning to go on vacation, I request you to approve this and to ask the management to
grant me a personal loan in the amount of $ ***.*** for my vacation expenditure.
I am willing to pay it back from my monthly salary.
Thank you for your prompt attention to this request.
Best wishes, Clive