Question

Mr. Weinstein has a savings account with a balance of $19,211.34. It pays 4% interest compounded daily.

a. What is his ending balance after three years, if no other deposits or withdrawals are made?


b. How much interest does he earn over the three years?

Answer 1

assuming 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 &\$19211.34\\ r=rate\to 4\%\to (4)/(100)\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{daily, thus 365} \end{array}\dotfill &365\\ t=years\dotfill &3 \end{cases}`

`A = 19211.34\left(1+(0.04)/(365)\right)^(365\cdot 3) \implies \stackrel{balance}{\boxed{A \approx 21660.58}}~\hfill \underset{interest}{\stackrel{21660.58~~ - ~~19211.34}{\boxed{\approx 2449.24}}}`