If i deposit $3,000$ dollars every year for $10$ years, with an annual compound of $10 \%$ return, what is the formula that I would use to figure this out?
I can't wrap my head around this. I have $3000 + 3000 \times 1.1 + 3000 \times 1.1$ and so forth for $10$ years. What is the simplified formula?
It is much easier if you consider the value of each deposit separately and add them up. It is $3000(1.1+1.1^2+\dots +1.1^{10})$, assuming you make the deposit at the beginning of the year and the withdrawal at the end of year $10$. The part in the parentheses is a geometric progression which can be summed, giving a final value of $3000\frac{1.1^{11}-1.1}{1.1-1}\approx 52593.50$