🚀 go-pugleaf

Siobhan Michaels wrote:

> Hey. i'm 15 and studying for exams at the mo. i've been doing some practice
> questions and i got stuck on this one:
> In 1997 a bank's interest charges were 1.65% per month. The interest was
> charged compound. How much is the interest rate per year (the APR)?
> The answer in the book was 21.7% but i can't figure out how they got that,
> so could someone please explain.

Yes.  Do you know what compounded means?  Lets say you start with X dollars
owed at the beginning of the first month.  At the end of the first month, you
will have accumulated 1.65% interest on that amount.  You will still owe the X
dollars and now owe and additional 0.0165*X.  So, you owe 1.0165*X.  Now, since
the interest is compounded, the next month you will pay interest on the total
amount you owe, not just on the original amount owed.  i.e. The interest will
not just be 0.0165*X, but will be 0.0165*(1.0165*X).  So, at the end of the
second month you will owe 1.0165*1.0165*X.  In general, after each month you
will owe 1.0165 times what you owed at the months beginning.  So, after N
months you will owe (1.0165)^N times as much as at the beginning of the N
months.   In particular, at the end of 12 months, you will owe (1.0165)^12 =
1.2169944... times what you owed at the years beginning.  This is approximately
21.7% interest per year.

> Also, i can't grasp the topic of surds and could anyone help me with that??

I don't know what a surd is.