sam is getting ready for a big date when he realizes that he has no money. his roommate, bill, also has no money, but he has a credit card. knowing that nobody will let sam use bills credit card, sam asks bill to pull out a cash advance for \$120.00. bill agrees under the condition that sam is responsible for all interest that accrues on the cash advance which is a 30\% interest rate, compounded monthly. the \$120 cash advance is repaid in monthly installments over 5 years. how much should bill ask sam to pay in interest for the cash advance?
a. \$3.88
b. \$112.80
c. \$120.00
d. \$232.80

Question

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": [ "Amortized Payment Calculation", "Cash Advance Interest" ], "new_concepts": [], "current_concepts": [ "Amortized Payment Calculation", "Cash Advance Interest", "Compound Interest" ] } ## Identify given parameters Using the *Amortized Payment Calculation* and *Cash Advance Interest* knowledge points $$ \begin{aligned} P &= \$120.00 \ r &= 30\% = 0.30 \ n &= 12 \text{ payments per year} \ t &= 5 \text{ years} \ N &= n \times t = 60 \text{ total payments} \ i &= \frac{r}{n} = \frac{0.30}{12} = 0.025 \text{ monthly interest rate} \end{aligned} $$ ## Calculate monthly payment Using the *Amortized Payment Calculation* knowledge point $$ \begin{aligned} M &= P \frac{i(1+i)^N}{(1+i)^N - 1} \ M &= 120 \frac{0.025(1.025)^{60}}{(1.025)^{60} - 1} \ (1.025)^{60} &\approx 4.39979 \ M &\approx 120 \frac{0.025 \times 4.39979}{4.39979 - 1} \approx 120 \frac{0.109995}{3.39979} \approx \$3.88 \end{aligned} $$ ## Calculate total interest paid Using the *Cash Advance Interest* knowledge point $$ \begin{aligned} \text{Total Payments} &= M \times N \approx 3.88 \times 60 = \$232.80 \ \text{Total Interest} &= \text{Total Payments} - P \ \text{Total Interest} &\approx 232.80 - 120.00 = \$112.80 \end{aligned} $$

a. $3.88

b. $112.80

c. $120.00

d. $232.80

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Amortized Payment Calculation" ] }

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Question

Explanation:

Identify given parameters

Calculate monthly payment

Calculate total interest paid

Answer: