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Answer to Question #70244 in Finance for Nick Mango

Question #70244
You went shopping a month ago, racking charges of $2,000 to your credit card along
the way. Then the credit card statement comes, and it says your minimum monthly
payment is only $40. Suppose you only pay the minimum payment of $40 every month.
If the stated interest rate is 24%/year, compounded monthly, how long does it take for
you to pay off your credit card debt? For simplicity, assume the first payment is due
immediately, and your credit card company starts charging you interest after the first
day of the first payment.
Expert's answer
Charges of $2,000 to your credit card, minimum monthly payment is $40,
interest rate is 24%/year, compounded monthly.
The time you need to pay off your credit card debt is:
P = r*PV*(1 + r)^n/((1 + r)^(n) - 1),
40 = 0.24/12*1960*(1 + 0.24/12)^n/((1 + 0.24/12)^n - 1),
40 = 39.2*1.02^n/(1.02^n - 1),
40*(1.02^n - 1) = 39.2*1.02^n,
0.8*1.02^n = 40,
1.02^n = 50,
n = 197.5 month or 16.5 years.

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