Answer
Each month deposit is \[\$704\], the amount of interest at the end of 40 years will be\[\$1,162,080\].
Work Step by Step
Compute the value of deposit by substituting the values in the formula as mentioned below:
\[\begin{align}
& P=\frac{1,500,000\left( \frac{0.0625}{12} \right)}{\left[ {{\left( 1+\frac{0.0625}{12} \right)}^{12\times 40}}-1 \right]} \\
& =\frac{\$1,500,000\times0.0052}{\left[{{\left(1+0.0052\right)}^{480}}-1\right]}\\&=\frac{\$7,800}{11.0795}\\&=\$704\end{align}\]
: Hence, the value of the deposit which is paid at the end of each month is \[\$704\]
Computation of the interest amount can be done by deducting the Principal amount (P) from the future value (A) of the loan. Compute the amount of interest using the equation as shown below:
\[\begin{align}
& \text{Amount of interest}=\text{Value of Annuity after 40 years}-\text{Amount deposited in 40 years} \\
& =\$1,500,000-\left(12\times40\times\$704\right)\\&=\$1,500,000-\$337,920\\&=\$1,162,080\end{align}\]
Hence, the amount of interest at the end of 40 years will be\[\$1,162,080\].
