Question

This month, your friend deposits $400 to save for a vacation. She plans to deposit 10% more each successive onth for the next 11 months. How much will she have saved after 12 deposits?

Answer 1

Neverminding for a second that she's depositing 10% of 400 every month

let's say, she goes to the bank, drops 400, and goes home and sits comfy for 12 months

now, the bank every month, is giving her 10%
how much is the amount at the end of the year? or at the 12th deposit?

well, is just a matter of compound interest

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{compounded amount}\\ P=\textit{original amount deposited}\to &\ 400\\ r=rate\to 10\%\to \frac{10}{100}\to &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{is every month, thus} \end{array}\to &12\\ t=years\to &1 \end{cases} \\\\\\ A=400\left(1+\frac{0.1}{12}\right)^{12\cdot 1}$