Chapter 5

# Chapter 5 - 1. Find the EAR in each of the following cases...

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1. Find the EAR in each of the following cases (Do not include the percent signs (%). Use 365 days in a year. Round your answers to 2 decimal places (e.g., 32.16)) : Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) 11.7 5 % Quarterly % 14.2 5 Monthly % 17.7 5 Daily % 13.7 5 Semiannually % Explanation: For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m )] m – 1 EAR = [1 + (0.1175 / 4)] 4 – 1 = 0.1228 or 12.28% EAR = [1 + (0.1425 / 12)] 12 – 1 = 0.1522 or 15.22% EAR = [1 + (0.1775 / 365)] 365 – 1 = 0.1942 or 19.42% EAR = [1 + (0.1375 / 2)] 2 – 1 = 0.1422 or 14.22% Calculator Solution: Enter 11.75% 4 NOM EFF

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C/Y Solve for 12.28% Enter 14.25% 12 NOM EFF C/Y Solve for 15.22% Enter 17.75% 365 NOM EFF
C/Y Solve for 19.42% Enter 13.75% 2 NOM EFF C/Y Solve for 14.22% 2. First National Bank charges 10.9 percent compounded monthly on its business loans. First United Bank charges 11.1 percent compounded semiannually. Requirement 1: Calculate the EAR for each bank. (Do not include the percent signs (%). Round your answers to 2 decimal places (e.g., 32.16).) EAR First National Bank % First United Bank %

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Requirement 2: As a potential borrower, which bank would you go to for a new loan? First United Bank Explanation: 1: For discrete compounding, to find the EAR, we use the equation: EAR = [1 + (APR / m )] m – 1 So, for each bank, the EAR is: First National: EAR = [1 + (0.109 / 12)] 12 – 1 = 0.1146 or 11.46% First United: EAR = [1 + (0.111 / 2)] 2 – 1 = 0.1141 or 11.41% 2: For a borrower, First United would be preferred since the EAR of the loan is lower. Notice that the higher APR does not necessarily mean the higher EAR. The number of compounding periods within a year will also affect the EAR. Calculator Solution: Enter 10.9% 12 NOM EFF C/Y
Solve for 11.46% Enter 11.1% 2 NOM EFF C/Y Solve for 11.41% 3. You want to buy a new sports coupe for \$75,300, and the finance office at the dealership has quoted you a 7.7 percent APR loan for 36 months to buy the car. Requirement 1: What will your monthly payments be? (Do not include the dollar sign (\$). Round your answer to 2 decimal places (e.g., 32.16).) Monthly payment \$ Requirement 2: What is the effective annual rate on this loan? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

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Effective annual rate % Explanation: 1: We first need to find the annuity payment. We have the PVA, the length of the annuity, and the interest rate. Using the PVA equation: PVA = C ({1 – [1/(1 + r ) t ]} / r ) \$75,300 = C [1 – {1 / [1 + (0.077/12)] 36 } / (0.077/12)] Solving for the payment, we get: C = \$75,300 / 32.05318 C = \$2,349.22 2: To find the EAR, we use the EAR equation: EAR = [1 + (APR / m )] m – 1 EAR = [1 + (0.077 / 12)] 12 – 1 EAR = 0.0798 or 7.98% Calculator Solution:
Enter 36 7.7% / 12 ±\$75,300 N I/Y PV PMT FV

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Solve for \$2,349.22 Enter 7.70% 12 NOM EFF
C/Y Solve for 7.98%

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## This note was uploaded on 02/24/2011 for the course ACCT 416 taught by Professor Staff during the Winter '08 term at USC.

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Chapter 5 - 1. Find the EAR in each of the following cases...

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