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 Bill’s 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?
The monthly interest rate is 30% ÷ 12 = 2.5%, and 5 years gives 60 monthly payments. For a loan of $120, the monthly payment is about $120(0.025) ÷ [1 − (1.025)^−60] = $3.88. The total paid is about 60 × $3.88 = $232.80, so the interest is $232.80 − $120 = $112.80. The correct choice is $112.80.
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