Suppose you have a $4,200 balance on a credit card with an interest rate of 1.26% per month, and
The minimum payment for any month is the amount of interest plus 1% of the principal balance. You
Find that if you don't make any more purchases on that card and make the minimum payment for 6
Months, you will have reduced your principle by $245.78. If the credit card company instead sets its
Minimum payment at interest plus 3% of the principal balance, how much more progress would you
Make after making minimum payments for 6 months?
A)$455.74
B)$487.64
C)$587.90
D)$701.52

Question

Quizplus · Accepted Answer

Explanation:The minimum payment for the first month is 1.26% of $4,200 + 1% of $4,200 = $54.60 + $42 = $96.60.The principal balance after the first month is $4,200 - $96.60 = $4,103.40.The minimum payment for the second month is 1.26% of $4,103.40 + 1% of $4,103.40 = $52.29 + $41.03 = $93.32.The principal balance after the second month is $4,103.40 - $93.32 = $4,010.08.The minimum payment for the third month is 1.26% of $4,010.08 + 1% of $4,010.08 = $50.93 + $40.10 = $91.03.The principal balance after the third month is $4,010.08 - $91.03 = $3,919.05.The minimum payment for the fourth month is 1.26% of $3,919.05 + 1% of $3,919.05 = $49.56 + $39.19 = $88.75.The principal balance after the fourth month is $3,919.05 - $88.75 = $3,830.30.The minimum payment for the fifth month is 1.26% of $3,830.30 + 1% of $3,830.30 = $48.19 + $38.30 = $86.49.The principal balance after the fifth month is $3,830.30 - $86.49 = $3,743.81.The minimum payment for the sixth month is 1.26% of $3,743.81 + 1% of $3,743.81 = $47.03 + $37.44 = $84.47.The principal balance after the sixth month is $3,743.81 - $84.47 = $3,659.34.The total amount of interest paid over the six months is $96.60 + $93.32 + $91.03 + $88.75 + $86.49 + $84.47 = $540.66.The total amount of principal paid over the six months is $4,200 - $3,659.34 = $540.66.If the credit card company instead sets its minimum payment at interest plus 3% of the principal balance, the minimum payment for the first month would be 1.26% of $4,200 + 3% of $4,200 = $54.60 + $126 = $180.60.The principal balance after the first month would be $4,200 - $180.60 = $4,019.40.The minimum payment for the second month would be 1.26% of $4,019.40 + 3% of $4,019.40 = $51.04 + $120.58 = $171.62.The principal balance after the second month would be $4,019.40 - $171.62 = $3,847.78.The minimum payment for the third month would be 1.26% of $3,847.78 + 3% of $3,847.78 = $48.49 + $115.43 = $163.92.The principal balance after the third month would be $3,847.78 - $163.92 = $3,683.86.The minimum payment for the fourth month would be 1.26% of $3,683.86 + 3% of $3,683.86 = $46.95 + $110.52 = $157.47.The principal balance after the fourth month would be $3,683.86 - $157.47 = $3,526.39.The minimum payment for the fifth month would be 1.26% of $3,526.39 + 3% of $3,526.39 = $44.42 + $105.79 = $150.21.The principal balance after the fifth month would be $3,526.39 - $150.21 = $3,376.18.The minimum payment for the sixth month would be 1.26% of $3,376.18 + 3% of $3,376.18 = $42.91 + $101.28 = $144.19.The principal balance after the sixth month would be $3,376.18 - $144.19 = $3,231.99.The total amount of interest paid over the six months would be $180.60 + $171.62 + $163.92 + $157.47 + $150.21 + $144.19 = $968.01.The total amount of principal paid over the six months would be $4,200 - $3,231.99 = $968.01.Therefore, the amount of progress made after making minimum payments for 6 months would be $968.01 - $540.66 = $427.35.

Suppose You Have a $4,200 Balance on a Credit Card