Question

Need help with this question !!!

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$10000\\ r=rate\to 8.9\%\to (8.9)/(100)\dotfill &0.089\\ t=years\dotfill &2 \end{cases} \\\\\\ A = 10000e^(0.089\cdot 2) \implies A=10000e^(0.178)\implies \boxed{A \approx 11948.25}`

yeap, he'll have enough, even some change for ice-cream too.

will the other bank be a better idea?

`~~~~~~ \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 9\%\to (9)/(100)\dotfill &0.09\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus two} \end{array}\dotfill &2\\ t=years\dotfill &2 \end{cases}`

`A = 10000\left(1+(0.09)/(2)\right)^(2\cdot 2) \implies A = 10000( 1.045)^(4)\implies \boxed{A \approx 11925.19}`

not really.