Albert loaned $850,000 to Batman on March 17. On January 9 of the following year, Batman paid to Albert the $49,000 of interest that had accumulated on the debt up to that time. What simple rate of interest was Albert charging on this loan?
A) 7.06%
B) 25.68%
C) 31.40%
D) 9.65%
E) 17.34%

Question

Quizplus · Accepted Answer

The interest ($49,000) is for a period shorter than a year (from March 17 to January 9, which is less than 12 months). To find the annual interest rate, we use the formula for simple interest: Interest = Principal × Rate × Time. Here, the principal is $850,000, and the interest is $49,000. The time is not a full year, but for the purpose of finding the annual rate, we consider the rate as if it were for a full year. Rearranging the formula to solve for the rate gives us Rate = Interest / (Principal × Time). Since the exact time in years is not specified and not needed to find the annual rate directly, we calculate the rate as $49,000 / $850,000 = 0.057647, or 5.76%. However, given the options and understanding the calculation might involve an approximation or a different understanding of the time period (assuming it might be considered for a full year for simplicity in this context), the closest match to the calculated rate is 7.06%, acknowledging a potential discrepancy in the calculation explanation.

Albert Loaned $850,000 to Batman on March 17