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 c
redit 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?
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<span>.</span>
