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. 5 full years go by before the $120 cash advance is repaid. how much should bill ask sam to pay in interest for the cash advance?

The options are:

a. $3.88 b. $112.80 c. $120.00 d. $232.80

Recall that to compute for the new amount of the original sum at a compound interest is A (t) = P (1 + r/n) ^ (nt) where P is the original amount, r is the interest rate, n is the number of times P is compounded each year, and t is the number of year. With this, the total amount owed by Sam in five full years becomes [ (120) (1 + 0.30/12) ^60 ]. The total interest is the difference between the original amount owed and the amount that needs to be paid over time. Thus, total interest is [ (120) (1 + 0.30/12) ^60 ] - 120 = 407.97. Therefore, the total interest is $407.97.