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Harper Engine Company needs $687,000 to take a cash discount of 150/15, net 70. A banker will loan the money for 55 days at an interest cost of $20,800.

a. What is the effective rate on the bank loan?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

b. How much would it cost (in percentage terms) if Harper did not take the cash discount but paid the bill in 70 days instead of 15 days?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

d. If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $687,000?
(Round your answer to 2 decimal places.)

e-1. What would be the effective interest rate in part d if the interest charge for 55 days were $12,600?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

Answer :

The effective rate on the bank loan is approximately 72.71%. The cost, in percentage terms of 70 days instead of 15 days is approximately 1.51%. Lower than the cost of not taking the discount (1.51%). Harper must borrow approximately $763,333.33. interest charge of $12,600.

A. The effective rate is: (given information)

  • Interest cost = $20,800
  • Loan period = 55 days
  • Loan amount = $687,000

Effective rate = (Interest cost / Loan amount) × (360 / Loan period)

Effective rate = ($20,800 / $687,000) × (360 / 55)

Effective rate = 0.1110 × 6.5455

Effective rate = 0.7271

B. The cash discount is: (given information)

  • Discount % = 1.50%
  • Discount period = 15 days
  • Net period = 70 days

Cost of not taking the discount = (Discount % / (100% - Discount %)) * (360 / (Discount period - Net period))

Cost of not taking the discount = (1.50% / (100% - 1.50%)) * (360 / (15 - 70))

Cost of not taking the discount ≈ 1.51%

C. Bank loan (72.71%) is lower than the cost of not taking the discount (1.51%).

D. The loan amount is: (given information)

  • Desired amount = $687,000
  • Compensating balance % = 10%

Loan amount = Desired amount / (1 - Compensating balance %)

Loan amount = $687,000 / (1 - 0.10)

Loan amount ≈ $763,333.33

E. The effective interest rate: (given information)

  • Interest cost = $12,600
  • Loan period = 55 days
  • Loan amount = $763,333.33

Effective rate = (Interest cost / Loan amount) × (360 / Loan period)

Effective rate = ($12,600 / $763,333.33) × (360 / 55)

Effective rate = 0.0165 × 6.5455

Effective rate = 0.1079

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