Chrissy currently has a credit card that charges 15 percent interest. She usually carries a balance of about $500. Chrissy has received an offer for a new credit card with a teaser rate of 3 percent for the first three months; after that, the rate increases to 19.5 percent. Assume that interest is compounded daily. What will her total annual interest be with her current card? What will her interest be the first year after she switches? Should she switch?

The provided solution is

Current card: P/Y = 12, C/Y = 365, N = 12, I/Y = 15, PV = 500, PMT = 0, FV = $580.90 The monthly interest charge on the old card is 580.90 500 = $80.90. Therefore, the annual interest cost is 80.90 12 = $970.80.

New card: P/Y = 12, C/Y = 365, N = 12, I/Y = 3, PV = 500, PMT = 0, FV = $515.23 During the teaser rate period, the monthly interest charge on the new card is 515.23 500 = $15.23. Therefore, the charge for 3 months is 15.23 3 = $45.69 P/Y = 12, C/Y = 365, N = 12, I/Y = 19.5, PV = 500, PMT = 0, FV = $607.62 After the rate increase, the monthly interest charge on the new card is 607.62 500 = $107.62. Therefore, the charge for 9 months is 107.62 9 = $968.58. The annual interest cost is 45.69 + 968.58 = $1014.27.

Chrissy should not switch to the new card.

WHY DO THEY MULTIPLY BY 12? Isn't $80.90 the interest for the year?