A local finance company quotes an interest rate of 19.7 percent on one-year loan
ID: 2773497 • Letter: A
Question
A local finance company quotes an interest rate of 19.7 percent on one-year loans. So, if you borrow $47,000, the interest for the year will be $9,259. Because you must repay a total of $56,259 in one year, the finance company requires you to pay $56,259/12, or $4,688.25 per month over the next 12 months.
No/Yes?
What rate would legally have to be quoted? (Round your answer as directed, but do not use rounded numbers in intermediate calculations. Enter your answer as a percent rounded to 2 decimal places (e.g., 32.16).)
What is the effective annual rate?
A local finance company quotes an interest rate of 19.7 percent on one-year loans. So, if you borrow $47,000, the interest for the year will be $9,259. Because you must repay a total of $56,259 in one year, the finance company requires you to pay $56,259/12, or $4,688.25 per month over the next 12 months.
Explanation / Answer
1) No, the interest rate on the loan is not 19.7%.
The interes rate is computed as follows:
2)
Compute the monthly Interest rate.
PMT = $4,688.25.
Nper = 12 months.
Rate = Rate(Nper, Pmt, PV) = =RATE(12,-4688.25,47000) = 2.881% or 0.02881
3)
Effective annual interest rate = 0.02881 * 12 = 0.3457 or 34.57%.
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