Answer: The effective annual rate on the loan can be calculated using the formula:
Effective Annual Rate = (1 + (quarterly interest rate))^4 - 1
First, let's calculate the quarterly interest rate. Since the bank charges $250 in interest at the end of each quarter, we can divide this amount by the loan principal of $10,000 to get the quarterly interest rate:
Quarterly interest rate = $250 / $10,000 = 0.025
Next, let's calculate the effective annual rate using the formula mentioned earlier:
Effective Annual Rate = (1 + 0.025)^4 - 1
Simplifying this equation gives us:
Effective Annual Rate = (1.025)^4 - 1
Calculating the value inside the parentheses:
Effective Annual Rate = 1.1006 - 1
Finally, subtracting 1 from 1.1006 gives us the effective annual rate on the loan:
Effective Annual Rate = 0.1006 or 10.06%
Therefore, the effective annual rate on the loan is 10.06%. This means that if you borrow $10,000 from People's Bank and make interest payments of $250 at the end of each quarter, you will effectively be paying an annual interest rate of 10.06% on the loan.