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, because you just received an offer in the mail to transfer your $ 10,000 balance from your current credit card, which charges an annual rate of 18.6 %, to a new credit card charging a rate of 8.6 %. How much faster could you pay the loan off by making your planned monthly payment of $ 160 with the new card? What if there was a 3 % transfer fee charged on any balances transferred?

Step by step solution

Explanation / Answer

Under old credit card Total balance = C*[1-(1/{1+R}^t]/R C= Monthly payment R= Rate of return for the period t= number of periods Monthly rate = Annual rate/12 Monthly rate = 18.60%/12 = 1.55% Total balance = C*[1-(1/{1+R}^t]/R 10000 = 160*[1-(1/{1+0.0155}^t]/0.0155 0.96875 =[1-(1/{1+0.0155}^t] 1/(1.0155^t) = 0.03125 (1.0155^t) = 32 t= 225 periods Under new credit card Total balance = C*[1-(1/{1+R}^t]/R C= Monthly payment R= Rate of return for the period t= number of periods Monthly rate = Annual rate/12 Monthly rate = 8.60%/12 = 0.7167% Total balance = C*[1-(1/{1+R}^t]/R 10000 = 160*[1-(1/{1+0.007167}^t]/0.007167 0.447916 =[1-(1/{1+0.007167}^t] 1/(0.007167^t) = 0.5520833 (1.007167^t) = 1.181 t= 24 periods How much faster to play the loan off = Time with current annual rate/Time with new annual rate How much faster to play the loan off = 225/24 How much faster to play the loan off = 9.375 Times

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