cuhmoon wrote:
This maybe a foolish question but how does one know the amount was compounded for the second year also or that compounding needs to be done again on the amount?
Why isn't the solution just using the amount and adding x to the amount: (1.08x+x)
Dear
cuhmoon,
I'm happy to respond.
You may find this blog article helpful:
Compound Interest on the GMATMy friend, please don't be afraid of asking a question because it might appear "foolish." Every basic question you ask that gets answered by an expert will there to help dozens of other GC users who were afraid to ask that same question.
The big idea of compound interest is
interest on interest. If we compounded in the first year, and then stopped, that wouldn't be compound interest. The action of compounding is when new interest starts to accrue on interest already there.
If x is the initial amount, notice that 0.08x is 8% of x--that would be just the interest after one cycle, if the interest rate were 8%. If we want interest plus principal, we add x + 0.08x = 1x + 0.08x = 1.08x. That latter form, 1.08x is a 8% increase on a starting value of x; it's the value of interest plus principal after one cycle. Notice that the question very specifically says: "
One year later Alex deposited an additional x dollars into the account." In other words, this is not just a single one-time deposit of principal that is building up interest: instead, Alex put money in, let it build up interest, and then put more money in from the outside. After the first year, 1.08x was already in the account, after the interest was added, and then separate from the process of interest, Alex deposited another x of his own money into this same account. That's why we add 1.08x + x.
In order to understand all this, it's very helpful to understand percents and percent changes as
multipliers.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)