Chapter 8 - Personal Finance - Chapter Summary, Review, and Test - Review Exercises - Page 571: 65

The option-B is more economical and interest saved is $53,040. Advantage of Mortgage is that it makes easy to have home ownership and is a cost effective way of borrowing money. Disadvantage of mortgage is that in mortgage one has to pay more than the amount actually borrowed in the form of interest.

Option-A Compute the monthly payment for mortgage as shown below: \[\begin{align} & PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\ & =\frac{\$70,000\left(\frac{0.085}{12}\right)}{\left[1-{{\left(1+\frac{0.085}{12}\right)}^{-12\left(30\right)}}\right]}\\&=\frac{\$70,000\times0.0070}{\left[1-{{\left(1+\frac{0.085}{12}\right)}^{-12\left(30\right)}}\right]}\\&=\frac{\$495.8}{\left[1-{{\left(1.0071\right)}^{-360}}\right]}\end{align}\] \[\begin{align} & =\frac{\$495.8}{\left[1-0.0783\right]}\\&=\frac{\$495.8}{0.921}\\&=\$538.3\\&\simeq\$538\end{align}\] So, \[\begin{align} & \text{Total Amount }=PMT\times n\times t \\ & =\$538\times12\times30\\&=\$193,680\end{align}\] \[\begin{align} & \text{The Interest}=\text{Total}\,\text{amount}-\text{Principal} \\ & =\$193680-\$70,000\\&=\$123,680\end{align}\] Option-B Compute the monthly payment for mortgage as shown below: \[\begin{align} & PMT=\frac{P\left( \frac{r}{n} \right)}{\left[ 1-{{\left( 1+\frac{r}{n} \right)}^{-nt}} \right]} \\ & =\frac{\$70,000\left(\frac{0.08}{12}\right)}{\left[1-{{\left(1+\frac{0.08}{12}\right)}^{-12\left(20\right)}}\right]}\\&=\frac{\$70,000\times0.00667}{\left[1-{{\left(1+0.00667\right)}^{-12\left(20\right)}}\right]}\\&=\frac{\$466.9}{\left[1-{{\left(1.00667\right)}^{-240}}\right]}\end{align}\] \[\begin{align} & =\frac{\$466.9}{\left[1-0.2028\right]}\\&=\frac{\$466.9}{0.7972}\\&=\$585.6\\&\simeq\$586\end{align}\] So, \[\begin{align} & \text{Total Amount }=PMT\times n\times t \\ & =\$586\times12\times20\\&=\$140,640\end{align}\] \[\begin{align} & \text{The Interest}=\text{Total amount}-\text{Principal} \\ & =\$140,640-\$70,000\\&=\$70,640\end{align}\] Compute the interest difference between the two options as follows: \[\begin{align} & \text{Interest difference}=\text{Interest from option A}-\text{Interest from option B} \\ & =\$123,680-\$70,640\\&=\$53,040\end{align}\] Advantage of Mortgage is that it makes easy to have home ownership and is a cost effective way of borrowing money. Disadvantage of mortgage is that in mortgage one has to pay more than the amount actually borrowed in the form of interest.