Here is a simple interest word problem that I apparently got it wrong. The problem is this:
Isabel borrowed $8000$ dollars from a bank. If the interest is compounded $15$ percent monthly. How much money wil she owe after $6$ years if shee didn't make any payments?
My logic is this: Suppose that the first month had passed, I will pay $8000(1.15)$. Then, the second month has passed and I will have to pay $8000(1.15)^2$. This paddern will continue until the 6 years has passed. Since there are $12$ months in a year, there will be $6*12=72$ months. Therefore, my solution is $8000(1.15)^72=187643918$. However, the solution is $19567.36$, which in my oppinion, is wrong. The reason for this is the $15$ percent is compounded monthly, which means that every month, the bank will charge $15$ percent more than the previous month. Notice that they didn't say "15% interest anually compounded monthly" - if they did, then I would agree with their solution.
So, is my logic correct? Thanks for your time.
No, but when taking up a loan in a bank, that's exactly how the interest usually works. I would always expect, unless otherwise specified, that a bank's interest percentages are yearly, regardless of when it's compounded.
In much the same way that problem authors may sometimes assume people know how a standard deck of cards look (52 cards, four suits, etc.), this problem author assumed you knew how banks phrase their deals.