Question

Mr. and Mrs. Sanchez want to invest money for their child’s college education. They have decided to invest $2000 initially. If the investment is in an account that earns 8% annual interest, compounded yearly for 10 years, how much will their investment be worth at the end of the 10th year?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 2000\left(1+(0.08)/(1)\right)^(1\cdot 10)\implies A=2000(1.08)^(10) \implies A \approx 4317.85`