Answer
.(a)
Compute deposits at the end of each month using formula as shown below:
\[\begin{align}
& P=\frac{A\left( \frac{r}{n} \right)}{\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]} \\
& =\frac{\$1,000,000\left(\frac{0.08}{12}\right)}{\left[{{\left(1+\frac{0.08}{12}\right)}^{12\times40}}-1\right]}\\&=\frac{\$1,000,000\left(0.00667\right)}{\left[{{\left(1+0.00667\right)}^{480}}-1\right]}\\&\frac{\$6,670}{\left[{{\left(1.00667\right)}^{480}}-1\right]}\end{align}\]
\[\begin{align}
& =\frac{\$6,670}{24.31-1}\\&=\$286.14\\&\approx\$286\\\end{align}\]
(b)
Tax deferred IRA annuity
Compute taxes using the formulas as shown below:
\[\begin{align}
& \text{Tax deferred IRA annuity}=\text{Amount of deposit at the end of each month}\times n \\
& =\$286\times12\\&=\$3,432\end{align}\]
Therefore, the IRA (Individual Retirement Account) amounts to $\$3,432$.
Taxes with IRA:
Work Step by Step
