Question

How much money should be deposited today in an account that earns 5.5% compounded monthly so that it will accumulate to $12,000 in three​ years?

The amount of money that should be deposited is ​$

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill&12000\\ P=\textit{original amount deposited}\dotfill\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &3 \end{cases}`

`\bf 12000=P\left(1+(0.055)/(12)\right)^(12\cdot 3)\implies 12000=P(1.00458\overline{3})^(36) \\\\\\ \cfrac{12000}{(1.00458\overline{3})^(36)}=P\implies 10178.56\approx P`

Answer 2

MaybeIf you do 12,000 times 5.5 and didved by 100?

Explanation: