Final answer:
The effective annual rate on a People's Bank loan with quarterly interest payments of $250 on a $10,000 loan is approximately 10.38%, corresponding to answer (c).
Step-by-step explanation:
To calculate the effective annual rate (EAR) on the loan offered by People's Bank, we need to consider the interest payments made each quarter and then find the equivalent annual rate that would result in the same amount of interest paid over the year. The loan calls for four quarterly payments of $250 each, resulting in a total of $1,000 in interest over the year on a $10,000 principal.
Since the interest is paid quarterly, the EAR can be computed using the formula for the effective annual rate with quarterly compounding:
EAR = (1 + (i/n))^n - 1, where i is the nominal annual rate and n is the number of compounding periods per year.
First, we need to find the nominal annual rate by calculating the annual interest paid and dividing it by the principal: i = $1,000/$10,000 = 0.10 or 10%. Because there are four quarters in a year, n = 4.
The effective annual rate (EAR) is thus:
EAR = (1 + (0.10/4))^4 - 1
EAR = (1 + 0.025)^4 - 1
EAR = 1.025^4 - 1
EAR = 1.103812890625 - 1
EAR = 0.103812890625 or approximately 10.38%
So the EAR on the loan is about 10.38%, making the correct answer (c).