Question

Which is the better choice: $1000 deposited for a year at a rate of 4.8% compounded semiannually 19) or at a rate of 4.7% compounded quarterly?

Answer 1

`~~~~~~ \stackrel{\textit{\Large 4.8\% 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 &\$1000\\ r=rate\to 4.8\%\to (4.8)/(100)\dotfill &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &1 \end{cases}`

`A=1000\left(1+(0.048)/(2)\right)^(2\cdot 1)\implies \boxed{A\approx 1048.58}~~\textit{\Large \checkmark} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large 4.7\% quarterly}}{\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 &\$1000\\ r=rate\to 4.7\%\to (4.7)/(100)\dotfill &0.047\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &1 \end{cases} \\\\\\ A=1000\left(1+(0.047)/(4)\right)^(4\cdot 1)\implies \boxed{A\approx 1047.83}`