Question

Juan deposited $20,000 in a savings account with a 4.75% APR compounded quarterly.

Write an equation that models the amount of money Juan has in the account.

Answer 1

`~~~~~~ \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 &\$20000\\ r=rate\to 4.75\%\to (4.75)/(100)\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A = 20000\left(1+(0.0475)/(4)\right)^(4\cdot t) \implies A = 20000\implies A=20000(1.011875)^(4t)`