The following is a good APGP practice question from AJC. Personally, I feel that its well set and tests students on their concepts and understanding.

Mary has a monthly income of $4,000. She is considering applying for a car loan of$40,000 for 6 years which charges an interest rate of 3.00% per annum, compounded monthly. Interest is chargeable immediately when the loan sum is drawn out. The monthly repayment, \$$m$, is fixed throught out the loan tenure.

1. Show that the calculated loan balance at the end of the $n^(th)$ loan month, after the monthly repayment is made, is given by $40000(\frac {(401)}{400})^n-400m((\frac {401}{400})^n-1)$.
2. By legislation, banks can approve a car loan only if the monthly repayment does not exceed 15% of an applicant’s monthly income. Prove that Mary will not be able to apply for the car loan.

Do give it an attempt and see if you can show as required. Share with me if there are any doubts.