tim has four credit cards with the balances and aprs listed in the chart below. what will tims total monthly minimum credit card payment need to be to pay off all four credit cards in 24 months?

a. $118.24
b. $162.62
c. $163.00
d. $221.93

Question

tim has four credit cards with the balances and aprs listed in the chart below. what will tims total monthly minimum credit card payment need to be to pay off all four credit cards in 24 months?

a. $118.24
b. $162.62
c. $163.00
d. $221.93

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Amortization Formula Analysis", "Credit Card Amortization Formula", "Table Reading" ], "new_concepts": [], "current_concepts": [ "Amortization Formula Analysis", "Credit Card Amortization Formula", "Table Reading" ] } ## Extract data from the table Using the *Table Reading* knowledge point $$ \begin{aligned} &\text{Card A: } P_A = \$1,260.00, \quad r_A = 12\% = 0.12\ &\text{Card B: } P_B = \$900.00, \quad r_B = 18\% = 0.18\ &\text{Card C: } P_C = \$1,290.00, \quad r_C = 9\% = 0.09\ &\text{Card D: } P_D = \$1,200.00, \quad r_D = 16\% = 0.16\ &n = 24 \text{ months} \end{aligned} $$ ## Apply amortization formula Using the *Credit Card Amortization Formula* and *Amortization Formula Analysis* knowledge points $$ \begin{aligned} &M = P \cdot \frac{i(1+i)^n}{(1+i)^n - 1}, \quad i = \frac{r}{12}\ &M_A = 1260 \cdot \frac{0.01(1.01)^{24}}{(1.01)^{24} - 1} \approx 59.27\ &M_B = 900 \cdot \frac{0.015(1.015)^{24}}{(1.015)^{24} - 1} \approx 44.90\ &M_C = 1290 \cdot \frac{0.0075(1.0075)^{24}}{(1.0075)^{24} - 1} \approx 58.91\ &M_D = 1200 \cdot \frac{0.013333(1.013333)^{24}}{(1.013333)^{24} - 1} \approx 58.75 \end{aligned} $$ ## Sum the monthly payments Using the *Credit Card Amortization Formula* knowledge point $$ \begin{aligned} &M_{\text{total}} = M_A + M_B + M_C + M_D\ &M_{\text{total}} \approx 59.27 + 44.90 + 58.91 + 58.75 = 221.83 \end{aligned} $$

a. $118.24

b. $162.62

c. $163.00

d. $221.93

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Credit Card Amortization Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Extract data from the table

Apply amortization formula

Sum the monthly payments

Answer: