Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is not permissible for you to get a loan with usury even if you are going to get benefits from the money that you will borrow, because it is forbidden to deal with usury, as this is a major sin.
Allah says: "O you who believe! Be afraid of Allâh and give up what remains (due to you) from Ribâ (usury) (from now onward), if you are (really) believers." (Al-Baqarah 2:278)
Allah also says: "Those who eat Ribâ (usury) will not stand (on the Day of Resurrection) except like the standing of a person beaten by Shaitan (Satan) leading him to insanity. That is because they say: "Trading is only like Ribâ (usury)," whereas Allah has permitted trading and forbidden Ribâ (usury). So whosoever receives an admonition from his Lord and stops eating Ribâ (usury) shall not be punished for the past; his case is for Allâh (to judge); but whoever returns [to Ribâ (usury)], such are the dwellers of the Fire - they will abide."
(Al-Baqarah 2:275)
In addition to this, it is confirmed that "The Prophet (Sallallahu Alaihi wa Sallam) cursed the one who consumes Riba (interest and usury),the one who gives it to others, the one who writes it down and the one who witnesses it. He said "All of them are equal in sin." (Reported by Muslim.)
If you want to obtain this sum of money, then let it be by legitimate means, for instance to seek this loan from a person without any interest.
As regards your question "Is it right for a Muslim to pay…" the answer is that what is right and just is what is in accordance with Shariah, not what contradicts it.
Allah says: "Verily, Allâh enjoins Al-Adl (i.e. justice and worshipping none but Allâh Alone - Islâmic Monotheism) (An-Nahl 16:90)
Allah also says: "Say (O Muhammad SAW): My Lord has commanded justice" (Al-A'raf 7:29)
Getting a loan with interest is contrary to Shariah, so it is not at all just and right to avail of it.
Allah knows best.