If you invest $1000 at 5.7% interest compounded quarterly, and you deposit $1000 each year, in how many years will you have a total of $1,000,000?
It's not difficult to set up the problem without the additional $1000 each year, but with it, I'm lost.
Assuming youdollars at the start of that year, let's try to find the amount we have at the end of the year:
at the end of each quarter, we multiply by 1.057,
hence, at the end of the year we have:. Our goal is to find n for which
.
This is difference equation which looks like:whose solution is of the form
(A, r and C are constants). To find these, solve first for
. You get A and r. Then plug in what you got in the initial equation to find C.
Now that you have the closed form, you can solve for
hope this helps
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