A local finance company quotes an interest rate of 15.8 percent on one-year loan
ID: 2817231 • Letter: A
Question
A local finance company quotes an interest rate of 15.8 percent on one-year loans. So, if you borrow $35,000, the interest for the year will be $5,530. Because you must repay a total of $40,530 in one year, the finance company requires you to pay $40,530/12, or $3,377.50 per month over the next 12 months.
What rate would legally have to be quoted? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) APR% =
What is the effective annual rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) EAR% =
Explanation / Answer
Annual effective rate
Interest charged = 5530
Total instalment amount = 40530
APR = 5530/40530
APR = 13.6%
Effective annual interest rate = (1 + (nominal rate / number of compounding periods)) ^ (number of compounding periods) - 1
Nominal rate = 15.8 %
N = 12
EAR% = (1+15.8/1)^1 – 1 = 15.8%
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