Time Value of Money Problem

Question

Beverly Hills started a paper route on January 1, 2009. Every three months, she deposits $1200 in her bank account, which earns 8 percent annually but is compounded quarterly. How much will she have on December 31, 2012?

Answer 1

Every 3 months she deposits $1200 dollars.  

Every 3 months (which would be quarterly) she earns interest.  The rate at which she earns interest is going to be 1/4 of 8%.

 

This means every 3 months she will earn 2% interest.  Now, the question is when we assume she first puts money into the account.  If she started on January 1st  2009, then I think it is safe to assume it will be 3 months before she deposits any money.  On April 3rd she will deposit the first $1200.  (Which is also the time of 1 quarter).  

 

1 quarter later on July 1st, she deposits $1200 again.  However, because she had $1200 in there for the duration of this quarter, she earns 2% interest on the $1200 already in there.

The interest she earned is 1200 * 0.02, or 24 dollars. With her newest deposit she will have $2424.

The 3rd quarter she will earn interest on $2424 AND deposit another 1200.

We can solve the problem until we reach December 31 2012.

I'm sure there is also an equation that follows this, but I do not know it off the top of my head.