Your Christmas ski vacation was great, but it unfortunately ran a bit over budge
ID: 2617891 • Letter: Y
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 $12,200 balance from your current credit card, which charges an annual rate of 20 percent, to a new credit card charging a rate of 10.6 percent.
How much faster could you pay the loan off by making your planned monthly payments of $235 with the new card? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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.)
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 $12,200 balance from your current credit card, which charges an annual rate of 20 percent, to a new credit card charging a rate of 10.6 percent.
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 10.6%/12 = .883%
while putting all the values
12200 = 235 * ( 1 - (1.00833)^(-n))/.00883
1.00883^(-n) = .5414
n* ln(1.00883) = .6136
n = 69.77 months (it will be fully paid on 70th month)
in second case
r = 20%/12 = 1.67%
12200 = 235 * (1 - 1.0167^(-n))/.0167
n * ln(1.0167) = 2.0044
n = 121.26 months ( it will be fully paid on 122th month)
With new card one can pay 51.49 months earlier.
If 1% fee charged then new amount need to paid using new card = 12200 * 1.01 = $ 12322
12322 = 235 * ( 1 - (1.00833)^(-n))/.00883
1.00883^(-n) = .5368
n* ln(1.00883) = .622069
n = 70.73 months
So, with new card one can pay 50.53 months earlier.
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