Solve the problem. Assume no new purchases are made with the credit card.
-The annual interest rate on a credit card is 16.99%. If a payment of $100.00 is made each month, how long will it take to pay off an unpaid balance of $1746.42?
A) 15 months
B) 23 months
C) 21 months
D) 20 months

Question

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The correct answer is C.The monthly interest rate is 16.99% / 12 = 1.416%. The monthly payment is $100.00. The unpaid balance after the first month is $1746.42 * (1 + 0.01416) - $100.00 = $1652.67. The unpaid balance after the second month is $1652.67 * (1 + 0.01416) - $100.00 = $1560.62. The unpaid balance after the third month is $1560.62 * (1 + 0.01416) - $100.00 = $1470.27. The unpaid balance after the fourth month is $1470.27 * (1 + 0.01416) - $100.00 = $1381.62. The unpaid balance after the fifth month is $1381.62 * (1 + 0.01416) - $100.00 = $1294.67. The unpaid balance after the sixth month is $1294.67 * (1 + 0.01416) - $100.00 = $1209.42. The unpaid balance after the seventh month is $1209.42 * (1 + 0.01416) - $100.00 = $1125.87. The unpaid balance after the eighth month is $1125.87 * (1 + 0.01416) - $100.00 = $1043.92. The unpaid balance after the ninth month is $1043.92 * (1 + 0.01416) - $100.00 = $963.57. The unpaid balance after the tenth month is $963.57 * (1 + 0.01416) - $100.00 = $884.82. The unpaid balance after the eleventh month is $884.82 * (1 + 0.01416) - $100.00 = $807.67. The unpaid balance after the twelfth month is $807.67 * (1 + 0.01416) - $100.00 = $732.12. The unpaid balance after the thirteenth month is $732.12 * (1 + 0.01416) - $100.00 = $658.17. The unpaid balance after the fourteenth month is $658.17 * (1 + 0.01416) - $100.00 = $585.82. The unpaid balance after the fifteenth month is $585.82 * (1 + 0.01416) - $100.00 = $515.07. The unpaid balance after the sixteenth month is $515.07 * (1 + 0.01416) - $100.00 = $445.92. The unpaid balance after the seventeenth month is $445.92 * (1 + 0.01416) - $100.00 = $378.37. The unpaid balance after the eighteenth month is $378.37 * (1 + 0.01416) - $100.00 = $312.42. The unpaid balance after the nineteenth month is $312.42 * (1 + 0.01416) - $100.00 = $248.07. The unpaid balance after the twentieth month is $248.07 * (1 + 0.01416) - $100.00 = $185.32. The unpaid balance after the twenty-first month is $185.32 * (1 + 0.01416) - $100.00 = $124.17. The unpaid balance after the twenty-second month is $124.17 * (1 + 0.01416) - $100.00 = $64.62. The unpaid balance after the twenty-third month is $64.62 * (1 + 0.01416) - $100.00 = $4.77. The unpaid balance after the twenty-fourth month is $4.77 * (1 + 0.01416) - $100.00 = -$90.58. Therefore, it will take 21 months to pay off the unpaid balance of $1746.42.

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