Question

An investment company pays 8% compounded semiannually.You want to have $19,000 in the future. (A) how much should you deposit now to have the amount 5 years from now

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill&19000\\ P=\textit{original amount deposited}\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases}`

`\bf 19000=P\left(1+(0.08)/(2)\right)^(2\cdot 5)\implies 19000=P(1.04)^(10) \\\\\\ \cfrac{19000}{1.04^(10)}=P\implies 12835.72\approx P`