Your Christmas ski vacation was great, but it unfortunately ran a bit over budge

Question

Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $12,000 balance from your current credit card, which charges an annual rate of 19.8 percent, to a new credit card charging a rate of 10.4 percent.

How much faster could you pay the loan off by making your planned monthly payments of $225 with the new card? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

What if there was a 2 percent fee charged on any balances transferred? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $12,000 balance from your current credit card, which charges an annual rate of 19.8 percent, to a new credit card charging a rate of 10.4 percent.

Explanation / Answer

Solution:

FVA = A [ ( 1+r)n -1] / r

12,000 = 225 [ ( 1+0.104)n -1] / 0.104

1248 = 225[ 1.104n -1]

1.104n ?-1 = 5.546

1.104n = 6.546

n log 1.104 = log 6.546

n = 18.98 months

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If there was a 2 percent fee charged on any balances transferred

The rate of interest will be 12.40 %

12,000 = 225 [ ( 1+0.1240)n -1] / 0.1240

1488 = 225 [( 1.1240n -1]

1.1240n -1 = 6.6133

1.1240n = 7.6133

n = 17.36 months

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