Question

Nancy is investing 20,000 in an account paying 7.25% interest compounded weekly. What would Nancy account balance be in 24 years?

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}\dotfill &\$20000\\ r=rate\to 7.25\%\to (7.25)/(100)\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, fifty two times} \end{array}\dotfill &52\\ t=years\dotfill &24 \end{cases}`

`\bf A=20000\left(1+(0.0725)/(52)\right)^(52\cdot 24)\implies A\approx 20000(1.001394)^(1248) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 113776.1384~\hfill`