Answer
$3,653,860
Work Step by Step
Compute the value of deposit, which is paid monthly using the equation as shown below:
\[\begin{align}
& P=\frac{A\left( \frac{r}{n} \right)}{\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]} \\
& =\frac{\$4,000,000\left(\frac{0.085}{12}\right)}{\left[{{\left(1+\frac{0.085}{12}\right)}^{12\times45}}-1\right]}\end{align}\]
Simplify and solve the equation as follows:
\[\begin{align}
& P\approx \frac{\$4,000,000\times0.007083}{{{\left(1.007083\right)}^{540}}-1}\\&=\frac{\$28,329}{45.210892-1}\\&=\frac{\$28,329}{44.210892}\\&\approx\$641\end{align}\]
Compute the amount of interest using the equation as shown below:
\[\begin{align}
& \text{Amount of interest}=\text{Value of Annuity after 45 years}-\text{Amount deposited in 45 years} \\
& \text{= }\!\!\$\!\!\text{4,000,000}-\left(12\times45\times\$641\right)\\&=\$4,000,000-\$346,140\\&=\$3,653,860\end{align}\]
