Question

as a new years resolution, jimmy has agreed to pay off his 4 credit cards and completely eliminate his credit card debt within the next 12 months. listed below are the balances and annual percentage rates for jimmys credit cards. in order to pay his credit card debt off in the next 12 months, what will jimmys total minimum credit card payment be?

credit card	current balance	apr
b	$2,525.00	21%
c	$972.00	19%
d	$389.00	17%

a. $321.83
b. $361.45
c. $374.65
d. $411.25

Explanation:

Extract data from the table

Using the Table Reading and Annual Percentage Rate knowledge points

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State the monthly payment formula

To pay off each card completely in 12 months, we use the standard amortization formula for monthly payment \(M\):

$$ M = P \cdot \frac{i(1+i)^N}{(1+i)^N - 1} $$

where:

• \(P\) is the principal balance.
• \(i = \frac{r}{12}\) is the monthly interest rate.
• \(N = 12\) is the number of monthly payments.

Calculate monthly payment for each card

We compute the monthly payment for each of the four credit cards:

• Card A:

$$ i_A = \frac{0.16}{12} \approx 0.013333 $$

$$ M_A = 563 \cdot \frac{0.013333(1.013333)^{12}}{(1.013333)^{12} - 1} \approx \$51.08 $$

• Card B:

$$ i_B = \frac{0.21}{12} = 0.0175 $$

$$ M_B = 2525 \cdot \frac{0.0175(1.0175)^{12}}{(1.0175)^{12} - 1} \approx \$235.11 $$

• Card C:

$$ i_C = \frac{0.19}{12} \approx 0.015833 $$

$$ M_C = 972 \cdot \frac{0.015833(1.015833)^{12}}{(1.015833)^{12} - 1} \approx \$89.65 $$

• Card D:

$$ i_D = \frac{0.17}{12} \approx 0.014167 $$

$$ M_D = 389 \cdot \frac{0.014167(1.014167)^{12}}{(1.014167)^{12} - 1} \approx \$35.41 $$

Sum the monthly payments

We add the individual monthly payments to find Jimmy's total monthly payment:

$$ M_{\text{total}} = M_A + M_B + M_C + M_D $$

$$ M_{\text{total}} = 51.08 + 235.11 + 89.65 + 35.41 = \$411.25 $$

Answer:

• a. $321.83
• b. $361.45
• c. $374.65
• d. $411.25 (Correct answer)