Question

(#10) How do I check if this is right for Hugo?

Answer 1

you're correct that, since Hugo is charging Johnny $2000, so the amount invested will be 98000.

`~~~~~~ \stackrel{\textit{\Large Hugo}}{\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 &\$98000\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &15 \end{cases}`

`A=98000\left(1+(0.06)/(4)\right)^(4\cdot 15)\implies A=98000(1.015)^(60)\implies A\approx 239435.54 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \stackrel{\textit{\Large Hector}}{\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 &\$100000\\ r=rate\to 5.5\%\to (5.5)/(100)\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases} \\\\\\ A=100000\left(1+(0.055)/(12)\right)^(12\cdot 15)\implies A=100000\left( (2411)/(2400) \right)^(180)\implies A\approx 227758.38`

well, seems that even though Hugo is charging some Johnny, the returned amount is more than with Hector, so Johnny should give Hugo a call.