Question

You WANT to end up with a future

value of $10,000
invested at 4% interest compounded
quarterly for 10 years. How much
should you start with as principal?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 10000\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}`

`10000 = P\left(1+(0.04)/(4)\right)^(4\cdot 10) \implies 10000=P(1.01)^(40) \\\\\\ \cfrac{10000}{(1.01)^(40)}=P\implies 6716.53\approx P`