Question

how much money should be deposited today in an account that earns 6% compounded semiannually so that it will accumulate to $14,000 in three years

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\to &\$14000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to (6)/(100)\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\to &2\\ t=years\to &3 \end{cases} \\\\\\ 14000=P\left(1+(0.06)/(2)\right)^(2\cdot 3)\implies 14000=P(1.03)^6\implies \cfrac{14000}{1.03^6}=P`