Calculations on home mortgage payment
Your mortgage payments can be easily calculated with one formula.

Owning versus renting – which should you choose? And what are the costs associated with each choice? Here is a more detailed explanation of the example and various calculations from the previous article.

A Detailed Sample Calculation:

Our variables are defined as follows: Assume a $1 million dollar home with a 15% cash down-payment. And the following additional expenses. Note that the interest rate is fixed at 2%. This is much lower than the historical interest rate. And most home loans in Singapore are adjustable floating interest rates.

Assigned values to variables for calculating mortgage payments

Calculating Your Monthly Mortgage Payment

Your monthly mortgage payment will vary depending on the monthly interest rate, the number of monthly payments, and the total amount of (financed debt). Using the above figures, we can calculate these three variables:

Mortgage calculation

To get the monthly mortgage payment, plug in the values into the following equation:

Equation to calculate monthly mortgage payments

 

Separating the Principal and the Interest

The amount attributed to interest and to principal will change depending on how much of the principal is remaining for any given month. For the very first monthly mortgage payment, to get the portion attributable only to interest, you would multiple the monthly interest rate with the amount financed (at month 0); the remaining amount would then be applied to the principal.

First month principal and interest

At the end of the first month, your principal would be reduced by $1714. And the remaining amount of financed debt (at month 1) would be f1 = $848,286 (or $850,000 – $1714).

Using this new value, you will compute the amount attributable to interest for the second month (f1 * i = $848,286 * 0.0016667 = $1414). The amount attributed to principal would be $1716 (or $3130 – $1414).

The financed debt would be reduced by this new principal amount, and the cycle repeats itself. Although this may seem quite complicated, it is fairly easy to do in Excel.

 

Total Monthly Payment

To get your total monthly home payment, which is a more complete picture of what you would need to set aside for housing costs, you will add your mortgage payment to the monthly values for property tax, home insurance, and maintenance fees.

 

Total month home expenses

 

At the end of 10 years (at the 120th month), if your monthly home payment remained the same (assuming interest rates did not adjust, and property tax and insurance did not increase with inflation), then the total amount you paid is $429,600 (or $3580 * 120).

Your total remaining debt would be $622,581, and you will have $377,419 in equity. This equity is the sum of $227,419 from monthly payments and $150,000 from your initial down-payment.

At the end of 30 years (at the 360th month), assuming the monthly home payment remained constant, you would have paid a total of $1,288,800. Of that amount, $850,000 (66%) was the size of the loan, and $438,800 is the amount of the interest you paid. But this does not take into account a rise in interest rates or the effects of inflation.

The effects of interest rates:

Most people agree that interest rates will rise again. And a very slight change in interest rates can greatly increase your monthly mortgage payments. For example, if interest rates rise to 4% or 6%, your monthly mortgage payment (not including tax, insurance, or service fees) would increase to $4039 or $5066, respectively. At the end of 30 years, you will have paid $1,454,040 or $1,823,760, respectively. And that means half of what you pay could be on interest alone.

The effects of Inflation:

Even relatively low inflation rates will likely increase the amount of insurance, property tax, and maintenance fees you will need to pay, thus adding to the total monthly home payment.

 

In Conclusion:

I know that there are still a lot of other issues to consider. And we haven’t even discussed refinancing or second mortgages, which a lot of people will take up, especially when interest rates rise. But I just wanted to lay out a very simple and quick way of estimating the true cost of home ownership.

My intentions for these posts are merely to demonstrate that:

  1. The choice to own versus rent is not so black-and-white as everyone makes it out to be;
  2. That renting is not the same as “flushing money down a toilet”;
  3. That owning a home with a mortgage is very similar to renting, but instead of renting from a landlord, you are renting money from a bank or government; and
  4. Mostly importantly, that choosing to buy a property is complicated. You should take your time, do your research, and buy less than what you can truly afford. Even if interest rates and inflation remain low, your life circumstances can change. And you don’t want to be forced to sell out of distress or desperation.  

 

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