Why does the highest percent profit occur with the smallest annual interest rate?

This is so because the higher the interest rate the lower the profit and the higher the total expenses and the percentage profit = (Profit/Expenses) × 100

Step-by-step explanation:

Question;

It is desired to find out the monthly percentage profit made to help decide the best loan option

Part A

Given that the monthly operating cost of the gym is 5,000 and the monthly sales is 7,500

Let 'I' represent the monthly interest paid on the loan, we have;

The percentage profit = Profit/(Total expenses) × 100

The total expenses = I + 5000

Profit = Sales - The total expenses

∴ Profit = 7,500 - (I + 5,000) = 2,500 - I

The percentage profit, P = (2,500 - I)/(5,000 + I) × 100

Therefore, as the interest rate becomes smaller, the numerator of the function for the percentage profit approaches its maximum value of 2,500 and the denominator approaches the minimum value of 5,000 and the percentage profit therefore, approaches the maximum value

Therefore;

The highest percentage profit occurs at the smallest interest rate.