A Manager wants to sell her wares on credit, giving customers six months in whic

Question

A Manager wants to sell her wares on credit, giving customers six months in which to pay. However, she will have to secure a bank loan so that she can provide financing to her customers. The bank will charge an APR of 12% that will be compounded quarterly. She wants to quote an APR to her customers based on the effective semi-annual rate that will exactly cover her financing costs.

A. What is this effective semi-annual rate?

B. What is the APR she should quote to her customers?

C. What is this effective annual rate (APY)? Is this different from the effective annual rate she is paying to the bank?

Explanation / Answer

A))

Suppose she enters on credit of $100, hence she has to take $100 from the bank. which will be equal to 100*(1+12%/4)^2 = 106.09.

Hence she will collect $106.09 for credit of every $100. Hecne effective annual rate = 106.09 - 100 = 6.09%

B))

APR she has to give her customers will be (((112.5509/100)^(1/2))-1)*2% = 12.18%

C))

Effective APY = (100*(1+12%/4)^4) - 100 = 12.5509%

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