Ellen has maxed out her credit card at $11,500 and vows not to make any other credit card
Purchases. Her credit card company charges 1.23% interest per month, and the minimum monthly
Payment is all interest due plus 4% of the principal balance. How much of the balance can Ellen pay
Down if she pays the minimum payment only for 4 months?
A)$141.45
B)$565.80
C)$1,732.52
D)$1,325.54

Question

Quizplus · Accepted Answer

First, we need to calculate the interest charged per month:
$11,500 x 1.23% = $141.45

For the first month, Ellen's minimum payment would be:
$11,500 x 0.04 + $141.45 = $585.95

This means that only $444.50 ($585.95 - $141.45) will be applied to the principal balance. So her new balance would be:
$11,500 - $444.50 = $11,055.50

For the second month, the interest charged would be:
$11,055.50 x 1.23% = $136.01

Ellen's minimum payment for the second month would then be:
$11,055.50 x 0.04 + $136.01 = $507.44

Again, only $371.43 ($507.44 - $136.01) will be applied to the principal balance. So her new balance would be:
$11,055.50 - $371.43 = $10,684.07

We can repeat this process for the third and fourth months:

Third month:
Interest charged: $131.49
Minimum payment: $10,684.07 x 0.04 + $131.49 = $483.96
Balance after payment: $10,299.60

Fourth month:
Interest charged: $126.92
Minimum payment: $10,299.60 x 0.04 + $126.92 = $452.56
Balance after payment: $9,923.08

At the end of the fourth month, Ellen's balance would be $9,923.08. So she was able to pay down $11,500 - $9,923.08 = $1,576.92 of the balance. However, the answer choices are not exact, so we need to choose the one that is closest to this amount. The closest answer is C ($1,732.52). Ellen's minimum payment for the first month would be:
$11,500 * 0.0123 + $11,500 * 0.04 = $575

This means she only pays $575 and $11,500 - $575 = $10,925 remains as the new balance for the next month.

For the second month, the minimum payment would be:
$10,925 * 0.0123 + $10,925 * 0.04 = $543.63

This means Ellen pays $543.63, and $10,925 - $543.63 = $10,381.37 remains as the new balance for the third month.

For the third month, the minimum payment would be:
$10,381.37 * 0.0123 + $10,381.37 * 0.04 = $512.91

This means Ellen pays $512.91, and $10,381.37 - $512.91 = $9,868.46 remains as the new balance for the fourth month.

For the fourth month, the minimum payment would be:
$9,868.46 * 0.0123 + $9,868.46 * 0.04 = $481.53

This means Ellen pays $481.53, and $9,868.46 - $481.53 = $9,386.93 remains as the new balance after the fourth month.

Adding up all of her payments over the four months, Ellen would have paid a total of:
$575 + $543.63 + $512.91 + $481.53 = $2,113.07

Therefore, Ellen can pay down $11,500 - $9,386.93 = $2,113.07 in four months by paying the minimum payment only. So, the answer is C.

Ellen Has Maxed Out Her Credit Card at $11,500 and Vows