Question

Find the balance in an account with $4,250 principal earning 3% interest compounded quarterly

after 12 years. Round your answer to the nearest hundredth.
**show work plz

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4250\\ r=rate\to 3\%\to (3)/(100)\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &12 \end{cases}`

`\bf A=4250\left(1+(0.03)/(4)\right)^(4\cdot 12)\implies A=4250(1.0075)^(48)\implies \stackrel{\textit{rounded up}}{A=6083.47}`