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Jan 9, 2024

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W ORKSHEETS EAR/APR/Periodic Rate Worksheet A bank charges a monthly interest rate of 1% for car loans. If I take out a loan of $15,000, how much interest will I owe during the first month? Answer: Principal x Interest Rate $15,000 x 0.01 = $150 It would be unusual for a bank to quote a monthly interest rate. Instead, they quote an annual rate. How would this bank quote the 1% monthly periodic rate as an annual rate if they were quoting it as an APR with monthly compounding? Answer: 0.01 x 12 = 12% APR monthly comp How would they quote it as an EAR? Answer: ( 1.01^12) – 1 = 12.68% Convert the following APRs to periodic rates: 9% APR with weekly compounding: 0.09/52 = 0.00173 = 0.173% 8% APR with monthly compounding: 0.08/12 = 0.00666 = 0.666% Convert the following periodic rates to APRs: 0.5% per month: 0.005 x 12 = 0.06 = 6.0% 0.1% per week: 0.001 x 52 = 0.052 = 5.2% Convert the following periodic rates to EARs: 0.3% per month: (1.003^12) – 1 = 3.66% 0.2% per week: (1.002^52) – 1 = 10.95% Convert the EARs to monthly periodic rates: 6.0% EAR: 1.06^(1/12) – 1 = 0.00486 = 0.486% 4.5% EAR: 1.045^(1/12) – 1 = 0.00367 = 0.367% Convert 5.75% APR (weekly compounding) to an EAR:
W ORKSHEETS First, convert to weekly periodic rate: 0.0575/52 = 0.0011057692 Then convert weekly period rate to an EAR: (1.001105769 52 ) – 1 = 0.0592 = 5.92% Convert 9.00% EAR to an APR with monthly compounding: First, convert to monthly periodic rate: 1.09 1/12 – 1 = 0.007202 Then convert the monthly period rate to an APR 0.007202 x 12 = 0.0865 = 8.65%.
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