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 $12,800 balance from your current credit card, which charges an annual rate of 20.6 percent, to a new credit card charging a rate of 11.2 percent. How much faster could you pay the loan off by making your planned monthly payments of $265 with the new card? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Number of months 39.3 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

Formula for loan amortization = A= [i*P*(1+i)^n]/[(1+i)^n-1] Amt $ A = periodical installment 265 P=Loan amount = 12,800 i= interest rate per period = 1.7167% n=total no of payments ? 265=0.017167*12800*1.017167^n/(1.017167^n-1) so 1.017167^n/(1.017167^n-1)=                1.2060 n = approx 103.8 months When the interest rate is 11.2% pa. The rate per month =0.9333% 265=0.009333*12800*1.009333^n/(1.009333^n-1) or 1.009333^n/(1.009333^n-1)=2.2183 n=64.5 months closely. So The reduction in months =103.8-64.5=                  39.30 months If there is 1% fee charged , then amount of loan would be =                14,080 So the equation will be 265=0.009333*14080*1.009333^n/(1.009333^n-1) or 1.009333^n/(1.009333^n-1)=2.0166 n=73.8 months approx So Reduction in months =103.8-73.8=                  30.00 months

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