The starting balance is $1,000
The simple interest rate is 10% per year.
There is also a 30% income tax on the interest earned annually.
Year 1:
[tex]\begin{gathered} 10\%\: interest=\frac{10}{100}\times\$1,000=\$100 \\ Overall\: balance=\$1,000+\$100=\$1,100 \\ 30\%\: tax=\frac{30}{100}\times\$100=\$30 \\ Overall\: balance\: after\: taxes=\$1,100-\$30=\$1,070 \end{gathered}[/tex]Year 2:
[tex]\begin{gathered} 10\%\: interest=\frac{10}{100}\times\$1,000=\$100 \\ Overall\: balance=\$1,070+\$100=\$1,170 \\ 30\%\: tax=\frac{30}{100}\times\$100=\$30 \\ Overall\: balance\: after\: taxes=\$1,170-\$30=\$1,140 \end{gathered}[/tex]Year 3:
[tex]\begin{gathered} 10\%\: interest=\frac{10}{100}\times\$1,000=\$100 \\ Overall\: balance=\$1,140+\$100=\$1,240 \\ 30\%\: tax=\frac{30}{100}\times\$100=\$30 \\ Overall\: balance\: after\: taxes=\$1,240-\$30=\$1,210 \end{gathered}[/tex]Year 4:
[tex]\begin{gathered} 10\%\: interest=\frac{10}{100}\times\$1,000=\$100 \\ Overall\: balance=\$1,210+\$100=\$1,310 \\ 30\%\: tax=\frac{30}{100}\times\$100=\$30 \\ Overall\: balance\: after\: taxes=\$1,310-\$30=\$1,280 \end{gathered}[/tex]Year 5:
[tex]\begin{gathered} 10\%\: interest=\frac{10}{100}\times\$1,000=\$100 \\ Overall\: balance=\$1,280+\$100=\$1,380 \\ 30\%\: tax=\frac{30}{100}\times\$100=\$30 \\ Overall\: balance\: after\: taxes=\$1,380-\$30=\$1,350 \end{gathered}[/tex]Therefore, the overall balance for 5 years after taxes would be $1350
