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 $12,500 balance from your current credit card, which charges an annual rate of 20.3 percent, to a new credit card charging a rate of 10.9 percent. How much faster could you pay the loan off by making your planned monthly payments of $250 with the new card? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Number of months What if there was a 1 percent fee charged on any balances transferred? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Number of months

Explanation / Answer

Will use presnet value of annuity formula to find this question

Present value of annuity = Periodic cashflow * ( 1 - (1+r)^(-n))/r

where r is 10.9%/12 = .908333%

while putting all the values

12500 = 250 * ( 1 - (1.00908333)^(-n))/.00908333

1.00908333^(-n) = .545834

n* ln(1.00908333) = .605441

n = 66.96 months

in second case

r = 20.3%/12 = 1.691667%

12500 = 250 * (1 - 1.01691667^(-n))/.01691667

n * ln(1.01691667) = 1.869722

n = 111.46 months

With new card one can pay 44.5 months earlier.

If 1% fee charged then new amount need to paid using new card = 12500 * 1.01 = $ 12625

12625 = 250 * ( 1 - (1.00908333)^(-n))/.00908333

1.00908333^(-n) = .541292

n* ln(1.00908333) = .613797

n = 67.88 months

So, with new card one can pay 43.58 months earlier.

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