you are considering two ways of financing a spring break vacation. You could put it on...

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you are considering two ways of financing a spring break vacation. You could put it on...

you are considering two ways of financing a spring break vacation. You could put it on your credit card, at 16% APR, compounded monthly, or borrow the money from your parents, who want an interest payment of 9% every six months. Which is a lower rate?

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Answer 1

Answer #1

Compounded monthly:

Effective annual rate = (1 + APR/n)ⁿ - 1

Effective annual rate = (1 + 0.16/12)¹² - 1

Effective annual rate = (1 + 0.013333)¹² - 1

Effective annual rate = 1.1723 - 1

Effective annual rate = 0.1723 or 17.23%

Compounded semi-annually:

APR = 9 * 2 = 18%

Effective annual rate = (1 + APR/n)ⁿ - 1

Effective annual rate = (1 + 0.18/2)² - 1

Effective annual rate = (1 + 0.09)² - 1

Effective annual rate = 1.1881 - 1

Effective annual rate = 0.1881 or 18.81%

16% APR, compounded monthly is the lower rate

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Answer 2

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