Question 6 (of 8) value: 10.00 points You receive a credit card application from

Question

Question 6 (of 8) value: 10.00 points You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 4 percent per year, compounded monthly for the first six months, increasing thereafter to 17.7 percent compounded monthly. Assume you transfer the $6,700 balance from your existing credit card and make no subsequent payments. How much interest will you owe at the end of the first year? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16) Interest References eBook&Resources; Learning Objective: 06-02 How loan payments are calculated and how to find the interest rate on a loan. Worksheet Section: 6.2 Valuing Level Cash Flows: Annuities and Perpetuities Difficulty: Intermediate

Explanation / Answer

Credit card outstanding amount = $6,700

Interest for first 6 months = .4% per year

Interest is compounded monthly

Credit card outstanding balance after 6 months will be calculated as under:

Outstanding Amount = Initial outstanding ( 1 + r )n

r = Monthly interest = 0.004/12

= 0.000333 p.m.

n = Number of times compounding is done = 6

Outstanding amount = 6,700 x ( 1 + 0.000333) 6

= 6,700 x ( 1.000333 )6

= 6,700 x 1.002

= $6,713.4

Hence, after 6 months credit card balance will become $6,713.4

Interest rate after 6 months = 17.7% per year

r = 0.177/12

= 0.01475 p.m.

Outstanding amount = 6,713.4 x ( 1 + 0.01475) 6

= 6,713.4 x ( 1.01475 )6

= 6,713.4 x 1.092

= $7,329.88

Hence, after 1 year, credit card balance will become $7,329.88

Hence, interest due on credit card after 1 year = 7,329.88 - 6,700

= $629.88

  

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