Smart Visa, Principal Card, and Acrobat Express are three credit card companies

Question

Smart Visa, Principal Card, and Acrobat Express are three credit card companies that charge different interest on overdue balances. Smart Visa charges 24% compounded daily, Principal Card charges 25% compounded weekly, and Acrobat Express charges 26% compounded monthly. What is the effective annual interest rate charged by each of the three companies? What is the effective semi-annual interest rate charged by each of the three companies? Which credit card company would you prefer? How much should the interest rate be for Smart Visa in order to break-even with Principal Card?

Explanation / Answer

a)Effective Annual Interest:

Smart Visa = [1+(0.24/365)]365 – 1 = 0.271149 or 27.1149%
Principal Card = [1+(0.25/52)]52 – 1 =0.283256 or 28.3256%
Acrobat Express = [1+(0.26/12)]12 – 1 = 0.293334 or 29.3334%

b)The question is a bit unclear. Effective semi-annual may mean two things. First, compounding semi-annually and second, the total period is semi-annual. I take it as total period to be semi-annual.

Number of days in semi-annual calculation = 183
Number of weeks = 26
Number of months = 6

Effective Semi-Annual Interest:

Smart Visa = [1+(0.24/183)]183 – 1 = 0.271049 or 27.1049%
Principal Card = [1+(0.25/26)]26 – 1 =0.282493 or 28.2493%
Acrobat Express = [1+(0.26/6)]6 – 1 = 0.289848 or 28.9848%

c)I would prefer Smart Visa as in each scenario, it’s effective interest rate is the lowest.

d)Interest rate required to break-even with Principal Card should equal the effective annual interest rate to Principal Card’s effective annual interest.

0.283256 = [1+(r/365)]365 – 1
r = 0.24945 or 24.945%

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