Question

$3,500 are deposited into an account with

a 5% interest rate, compounded quarterly.
Find the accumulated amount after
10 years.
Hint: A = P(1 + r/k)^kt

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 &\$3500\\ r=rate\to 5\%\to (5)/(100)\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &10 \end{cases}`

`A = 3500\left(1+(0.05)/(4)\right)^(4\cdot 10) \implies A = 3500( 1.0125)^(40)\implies A \approx 5752.67`