Question

Suppose that $9500 is placed in an account that pays 8% interest compounded each year.

Find the amount in the account at the end of 1 year.
Find the amount in the account at the end of 2 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 &\$9500\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}`

`\bf A=9500\left(1+(0.08)/(1)\right)^(1\cdot 1)\implies A=9500(1.08)\implies \boxed{A=10260} \\\\\\ \stackrel{\textit{after 2 years, t = 2}}{A=9500\left(1+(0.08)/(1)\right)^(1\cdot 2)}\implies A=9500(1.08)^2\implies \boxed{A=11080.8}`