I have the following problem: Determine the annual salary needed to repay a loan of $\$96,750$ with an interest rate of $4.5\%$ for a term of $20$ years.
What I did was first calculate the monthly payment which gave me the result $\$612.09$. I then multiplied this monthly payment by 12 to get my annual payment. This annual payment lasted me as a result $\$7,345.08$.
After doing some research, I found that in general, lenders recommend that the annual loan payment be no more than $30\%$ of a person's gross annual income. Of this, we will divide the annual payment by $0.3$ to get the annual salary required to repay the loan. After doing some research, I found that in general, lenders recommend that the annual loan payment be no more than 30% of a person's gross annual income. Of this, we will divide the annual payment by 0.3 to get the annual salary required to repay the loan. So, dividing the annual payment over $0.3$ I obtained that the required annual salary will be $\$24,483.6$
But I'm not sure if this is correct. Since I don't really know if the $30\%$ should be taken or another factor should be taken. Could you guide me?
I assume your arithmetic is correct. It is about right but I didn't check it in detail. The $30\%$ figure is not a mathematical one but a life experience one. If whoever gave you the problem did not specify how much of one's salary is allowed to be devoted to the loan you should carefully explain the assumption you are making, maybe even cite a place or two you found it, and turn in the result. I would bet some students do not consider the affordability but compute an annual salary of $\$7,345.08$ is required.