Question

Maxine deposited $1,000 into an account that pays 4.5% interest, compounded daily. At the end of six months, she has earned $12 in interest.

a. true b. false

Answer 1

since a year is 12 months thus six months is 6/12 of a year, now let's assume a year is 365 days.

`~~~~~~ \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 4.5\%\to (4.5)/(100)\dotfill &0.045\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\to (6)/(12)\dotfill &(1)/(2) \end{cases}`

`A = 1000\left(1+(0.045)/(365)\right)^{365\cdot (1)/(2)} \implies A = 1000\left( (73009)/(73000) \right)^(182.5) \\\\\\ A\approx 1022.75\hspace{5em}\underset{ \textit{earned interest} }{\stackrel{ 1022.75~~ - ~~1000 }{\approx \text{\LARGE 22.75}}}`