Question

Julie is opening a savings account at a bank that offers new clients 0.1% interest compounded quarterly. She deposits $1,700 when she opens the account.

Write an exponential expression in the form a(b)c, where b is a single value, to find the amount of money, in dollars, that will be in the account after t years. Round any decimals to the nearest hundred-thousandth and do not include dollar signs in the expression.

Answer 1

`\bf ~~~~~~ \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}\to &\$1700\\ r=rate\to 0.1\%\to (0.1)/(100)\to &0.001\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\to &4\\ t=years \end{cases} \\\\\\ A=1700\left(1+(0.001)/(4)\right)^(4\cdot t)\implies A=1700(1.00025)^(4t)`