Converging to Convergence?

📌 CONCEPT: A person will not be able to pay off the loan if the monthly payment is less than the initial loan amount multiplied by the monthly interest rate.

📐 RULE / FORMULA: The loan amount (A) at the end of each month can be calculated using the formula (A = P(1 + r)^n), where (P) is the initial loan amount, (r) is the monthly interest rate, and (n) is the number of months.

💡 WORKED EXAMPLE: Let's consider the loan amount to be Rs. 10000 and the monthly payment of Rs. 500. The monthly interest rate is 1% or 0.01. Using the formula, we can calculate the number of months it will take to pay off the loan. We can calculate the loan amount for each month and compare it with the monthly payment and find out that the loan will not be paid off.

⚠️ COMMON MISTAKE: Students may assume that the person will be able to pay off the loan if the monthly payment is more than the interest paid in a month, but this is not the case as the interest is compounded monthly.