Question

Can I please get help with this?

Answer 1

`~~~~~~ \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 &\$4000\\ r=rate\to 2.7\%\to (2.7)/(100)\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &10 \end{cases}`

`A = 4000\left(1+(0.027)/(2)\right)^(2\cdot 10)\implies A=4000(1.0135)^(20) \implies \boxed{A \approx 5230.40} \\\\[-0.35em] ~\dotfill`

`~~~~~~ \textit{Annual Percent Yield Formula} \\\\ ~~~~~~~~~~~~ \left(1+(r)/(n)\right)^(n)-1 ~\hfill \begin{cases} r=rate\to 2.7\%\to (2.7)/(100)\dotfill &0.027\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{\underline{semi-annually}, thus twice} \end{array}\dotfill &2 \end{cases} \\\\\\ \left(1+(0.027)/(2)\right)^(2)-1\implies 1.0135^2-1\approx 0.02718 ~~ \approx ~~ \stackrel{ 0.02718* 100 }{\boxed{2.718~\%}}`