Finance
Renting vs buying a property
This tool allows you to compare the financial outcome of buying a property, versus renting and investing the initial fees (down payment + taxes) in the stock market + investing the difference between the rent and the loan to pay each month. The stock market yield is assumed to be constant over the years.
How does it work?
This tool allows you to compare the financial outcome of buying a property, versus renting and investing the initial investment in the stock market and investing the difference between the rent and the loan to pay each month. The stock market yield is assumed to be constant over the years.
The property value is assumed to increase over the years, and the rent is also assumed to increase over the years.
\[\begin{align*}
& \text{Monthly loan payment} = \frac{{\text{Loan Amount} \times \left( \frac{{\text{Annual Interest Rate}}}{{12}} \right)}}{{1 - \left( 1 + \frac{{\text{Annual Interest Rate}}}{{12}} \right)^{-\text{Loan Term in Years} \times 12}}} \\
& \text{Initial Investment} = \frac{{\text{Down Payment} \times \text{Property Value}}}{{100}} \\
\end{align*}\]
How the total stock investment is calculated:
\[\begin{align*}
& \text{Total Stock Investment} = \text{Initial Investment} + \\
& \sum_{i=0}^{\text{Loan Term in Years} \times 12} \left( \frac{{\text{Yearly Property Taxes}}}{{12}} + \frac{{\text{Maintenance Costs}}}{{12}} \right) \times \text{Property Value} \\
& \qquad \times \left( 1 + \frac{{\text{Property Value Increase Rate} + \text{Inflation Rate}}}{{12}} \right)^i - \text{Monthly Rent} \times \left( 1 + \frac{{\text{Rent Increase Rate} + \text{Inflation Rate}}}{{12}} \right)^i \\
& \qquad \times \left( \frac{{\text{Loan Amount} \times \left( \frac{{\text{Annual Interest Rate}}}{{12}} \right)}}{{1 - \left( 1 + \frac{{\text{Annual Interest Rate}}}{{12}} \right)^{-\text{Loan Term in Years} \times 12}}} \right) \\
& \qquad \times \left( 1 + \frac{{\text{Stock Yield}}}{{12}} \right)^i
\end{align*}\]
How the property final value is calculated:
\[\text{Final Property Value} = \text{Property Value} \times \left(1 + \frac{{\text{Property Value Increase Rate} + \text{Inflation Rate}}}{{100}}\right)^{\text{Loan Term in Years}}\]