A local finance company quotes an interest rate of 19.5 percent on one-year loan
ID: 2771189 • Letter: A
Question
A local finance company quotes an interest rate of 19.5 percent on one-year loans. So, if you borrow $46,000, the interest for the year will be $8,970. Because you must repay a total of $54,970 in one year, the finance company requires you to pay $54,970/12, or $4,580.83 per month over the next 12 months.
1. What would the rate legally have to be quoted as?
2. What is the effective annual rate?
A local finance company quotes an interest rate of 19.5 percent on one-year loans. So, if you borrow $46,000, the interest for the year will be $8,970. Because you must repay a total of $54,970 in one year, the finance company requires you to pay $54,970/12, or $4,580.83 per month over the next 12 months.
Explanation / Answer
EMI = [P×r×(1+r)^n]÷[(1+r)^n-1]
$4,580.83 = [$46,000×r×(1+r)^12]÷[(1+r)^12-1]
Legal rate charged, r = 0.028532 or 2.85% per month
Effective annual rate = 34.2% (2.85%×12)
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