Question

2. Margie Spencer wants to have $100,000 in her savings account in 20 years. If her account pays 6.6% annual

interest compounded semiannually, how much must Margie deposit into her account now to meet her goal?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100000\\ P=\textit{original amount deposited}\\ r=rate\to 6.6\%\to (6.6)/(100)\dotfill &0.066\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}`

`100000=P\left(1+(0.066)/(2)\right)^(2\cdot 20)\implies 100000=P(1.033)^(40) \\\\\\ \cfrac{100000}{1.033^(40)}=P\implies 27288.97\approx P`