Question

Edward invested $1600 in a savings account for 8 years. At the end of 8 years, his savings account had $1920 in it.

If $1600 represents P, the principal amount, which percent represents the annual simple interest rate (r) that Edward earned after the 8 year (t) period?

Answer 1

`\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\$1920\\ P=\textit{original amount deposited}\to& \$1600\\ r=rate\to r\%\to (r)/(100)\\ t=years\to &8 \end{cases} \\\\\\ 1920=1600(1+r8)\implies \cfrac{1920}{1600}=1+8r\implies \cfrac{6}{5}=1+8r \\\\\\ \cfrac{6}{5}-1=8r\implies \cfrac{(6)/(5)-1}{8}=r\implies \cfrac{(1)/(5)}{8}=r\implies \cfrac{1}{40}=r \\\\\\ 0.025=r\implies r\%=100\cdot 0.025\implies r=\stackrel{\%}{2.5}`