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Friendly's quick loans, inc., offers you $5.25 today but you must repay $6.45 when you get your paycheck in one week (or else). what is the effective annual return friendly's earns on this lending business? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,
Friendly's quick loans, inc., offers you $5.25 today but you must repay $6.45 when you get your paycheck in one week (or else). what is the effective annual return friendly's earns on this lending business? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,e.g., 32.16.) effective annual return % if you were brave enough to ask, what apr would friendly's say you were paying? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.) annual percentage rate %
Final answer:The effective annual return (EAR) for Friendly's Quick Loans, Inc. is over 1,000,000%, while the annual percentage rate (APR) that might be advertised is 1188.564%. These figures highlight the very high costs of such short-term loans when extrapolated over a year.Explanation:To calculate the effective annual return (EAR) that Friendly's Quick Loans, Inc. earns on its lending business, we will use the formula for EAR which accounts for the effects of compounding interest over multiple periods within a year, even though in this case the loan is only for one week.Firstly, we find the interest for one period (one week):Interest = Final value - Initial valueInterest = $6.45 - $5.25 = $1.20The weekly return is then:Weekly return = Interest / Initial valueWeekly return = $1.20 / $5.25Weekly return = 0.22857 (or 22.857%)Since there are 52 weeks in a year, if we compound this weekly, the EAR is calculated as:EAR = (1 + Weekly return)^(52) - 1EAR = (1 + 0.22857)^(52) - 1EAR = 1,000,000+However, this result is not realistic due to the extremely high compounded interest, indicating that this type of loan would not be compounded weekly over a year. Therefore, EAR in this context should be interpreted with caution. The staggering number illustrates the high cost of such short-term loans when looked at on an annual basis.The annual percentage rate (APR) which Friendly's might advertise is the nominal interest rate for the year without taking compounding into account. It is simply the weekly rate multiplied by the number of weeks in a year:APR = Weekly return * 52APR = 22.857% * 52APR = 1188.564%The APR is the rate that would be quoted to consumers for comparison purposes....