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Compare the investment below to an investment of the same principal at the same rate compounded annually (look at picture below for details)

Compare the investment below to an investment of the same principal at the same rate-example-1

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so we have two investments, one compounding annually and another compounding semi-annually, let's check both


~~~~~~ \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 &\$5000\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &11 \end{cases} \\\\\\ A = 5000\left(1+(0.05)/(2)\right)^(2\cdot 11) \implies \boxed{A \approx 8607.86} \\\\[-0.35em] ~\dotfill


~~~~~~ \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 &\$5000\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &11 \end{cases}
A = 5000\left(1+(0.05)/(1)\right)^(1\cdot 11) \implies \boxed{A \approx 8551.70} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ semi-annually }{8607.86}~~ - ~~\stackrel{ annually }{8551.70} ~~ \approx ~~ \text{\LARGE 56.16}

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