Question

Wanting to see how they got to the answer for 43?

Answer 1

`~~~~~~ \stackrel{ \textit{\LARGE semiannually} }{\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 &\$10000\\ 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 &2 \end{cases}`

`A = 10000\left(1+(0.08)/(2)\right)^(2\cdot 2) \implies A\approx 11698.59\hspace{5em}\underset{ interest }{\stackrel{11698.59~~ - ~~10000 }{\approx \text{\LARGE 1698.59}}} \\\\[-0.35em] ~\dotfill`

`~~~~~~ \stackrel{ \textit{\LARGE quaterly} }{\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 &\$10000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quaterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}`

`A = 10000\left(1+(0.08)/(4)\right)^(4\cdot 2) \implies A \approx 11716.59\hspace{5em}\underset{ interest }{\stackrel{ 11716.59~~ - ~~10000 }{\approx\text{\LARGE 1716.59}}} \\\\[-0.35em] ~\dotfill\\\\ 1716.59~~ - ~~1698.59 ~~ \approx ~~ \text{\LARGE 18}`