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 $13,200 balance from your current credit card, which charges an annual rate of 21 percent, to a new credit card charging a rate of 11.6 percent.

How much faster could you pay the loan off by making your planned monthly payments of $285 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 2 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 $13,200 balance from your current credit card, which charges an annual rate of 21 percent, to a new credit card charging a rate of 11.6 percent.

Explanation / Answer

No of instalment to pay credit card @ 21% =

I =21/12

= 1.75

13200 = Annual instalment*PVIFA(i,n)

13200 =285*[1-{1/(1.0175)n}/0.0175]

46.32*0.0175 = 1-(1/{1.0175}n)

0.81 = 1-(1/{1.0175}n)

0.19 = 1/(1.0175)n

(1.0175)n = 5.263

N = 96 (Approxi.)

No of instalment to pay credit card @ 11.60% =

I =11.60/12

= 0.97

13200 = Annual instalment*PVIFA(i,n)

13200 =285*[1-{1/(1.0097)n}/0.0097

46.32*0.0097 = 1-(1/{1.0097}n)

0.45 = 1-(1/{1.0097}n)

0.55 = 1/(1.0097)n

(1.0097)n = 1.82

N = 62 (Approxi.)

Answer: 2.83 years [(96-62)/12] faster we can pay the loan off by making your planned monthly payments of $285 with the new card.

Note : We assume 2% charge is not paid upfront and becomes part of credit card.The answer would be the same as above in Part I if we assume charge is paid upfront and instalment amount is $285.

13200*(1.002) = Annual instalment*PVIFA(i,n)

13464=285*[1-{1/(1.0097)n}/0.0097

47.24*0.0097 = 1-(1/{1.0097}n)

0.458 = 1-(1/{1.0097}n)

0.542 = 1/(1.0097)n

(1.0097)n = 1.85

N = 64 (Approxi.)

Answer: 2.67 years [(96-64)/12] faster we can pay the loan off by making your planned monthly payments of $285 with the new card.

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