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A loan is offered with monthly payments and a 11.75 percent APR. What's the loan's effective annual rate (EAR)? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Effective annual rate. %

A loan is offered with monthly payments and a 11.75 percent APR. What's the loan's effective annual rate (EAR)? (Do not round intermediate calculations and round your final answer to 2 decimal places.) Effective annual rate. %

Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)
Pfin (with Mindtap, 1 Term Printed Access Card) (mindtap Course List)
7th Edition
ISBN:9780357033609
Author:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk
Publisher:Randall Billingsley, Lawrence J. Gitman, Michael D. Joehnk
Chapter7: Using Consumer Loans
Section: Chapter Questions
Problem 7FPE: Calculating interest and APR of installment loan. Assuming that interest is the only finance charge,...
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### Calculating the Effective Annual Rate (EAR) from APR with Monthly Payments When you take a loan, it is important to understand the actual cost of borrowing money. The Annual Percentage Rate (APR) is often quoted, but it doesn't reflect the true annual interest rate if payments are made more frequently than once a year. The Effective Annual Rate (EAR) gives a clearer picture of the real cost of borrowing. #### Problem Statement A loan is offered with monthly payments and a 11.75 percent APR. What’s the loan’s effective annual rate (EAR)? (Do not round intermediate calculations and round your final answer to 2 decimal places.) **Input Field:** - Effective Annual Rate: `[ ] %` #### Explanation The APR is the nominal interest rate, which does not take into account the effect of compounding within the year. The EAR, however, does take this compounding into account and provides a more accurate picture of the cost of the loan over a year. #### Formula To convert the APR to EAR, given monthly compounding, you can use the following formula: \[ \text{EAR} = \left(1 + \frac{\text{APR}}{n}\right)^{n} - 1 \] Where: - \(\text{APR}\) is the annual percentage rate (expressed as a decimal), - \(n\) is the number of compounding periods per year. For monthly payments, \(n = 12\). Given the APR of 11.75%, the calculation steps are: 1. Convert APR to decimal form: \(\text{APR} = 11.75\% = 0.1175\). 2. Apply the formula: \[ \text{EAR} = \left(1 + \frac{0.1175}{12}\right)^{12} - 1 \] 3. Perform the calculations: - Divide the APR by the number of periods: \(\frac{0.1175}{12} = 0.00979\) - Add 1 to this value: \(1 + 0.00979 = 1.00979\) - Raise to the power of 12: \((1.00979)^{12}\) - Subtract 1 from the result After calculating, you should round your final answer to 2 decimal places: \[ \text{EAR} \approx
Transcribed Image Text:### Calculating the Effective Annual Rate (EAR) from APR with Monthly Payments When you take a loan, it is important to understand the actual cost of borrowing money. The Annual Percentage Rate (APR) is often quoted, but it doesn't reflect the true annual interest rate if payments are made more frequently than once a year. The Effective Annual Rate (EAR) gives a clearer picture of the real cost of borrowing. #### Problem Statement A loan is offered with monthly payments and a 11.75 percent APR. What’s the loan’s effective annual rate (EAR)? (Do not round intermediate calculations and round your final answer to 2 decimal places.) **Input Field:** - Effective Annual Rate: `[ ] %` #### Explanation The APR is the nominal interest rate, which does not take into account the effect of compounding within the year. The EAR, however, does take this compounding into account and provides a more accurate picture of the cost of the loan over a year. #### Formula To convert the APR to EAR, given monthly compounding, you can use the following formula: \[ \text{EAR} = \left(1 + \frac{\text{APR}}{n}\right)^{n} - 1 \] Where: - \(\text{APR}\) is the annual percentage rate (expressed as a decimal), - \(n\) is the number of compounding periods per year. For monthly payments, \(n = 12\). Given the APR of 11.75%, the calculation steps are: 1. Convert APR to decimal form: \(\text{APR} = 11.75\% = 0.1175\). 2. Apply the formula: \[ \text{EAR} = \left(1 + \frac{0.1175}{12}\right)^{12} - 1 \] 3. Perform the calculations: - Divide the APR by the number of periods: \(\frac{0.1175}{12} = 0.00979\) - Add 1 to this value: \(1 + 0.00979 = 1.00979\) - Raise to the power of 12: \((1.00979)^{12}\) - Subtract 1 from the result After calculating, you should round your final answer to 2 decimal places: \[ \text{EAR} \approx
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