You’re shopping for a mortgage, and are presented with two different mortgage options, both with different rates and different features. The first thing you do is attempt to calculate the difference in cost between the two options.  What many will do is look at the difference in payment and then multiply that over the term of the mortgage, which then gives them the difference in cost between the two options.  This will not give you an accurate answer however, as the savings will be greater than this. 

There are two missing components:

  1. Balance at end of term.
  2. Time value of money

Let’s now look at each component separately.

Balance at end of term

Different rates will result in a different ending balance.  That is, how much money you will owe on your mortgage at the end of your term.  For example, let’s say you need a $500,000 mortgage, and you have a choice between 2.69% and 2.79%, both amortized over 25 years. At 2.79%, your monthly payment would be $2,312.68.  At 2.69%, it would be $2,287.42.  The difference in payment is $25.26.  If you were to multiply this over 60 months (5 years), the savings based on payment alone would be $1,515.60.    This is where most will stop when calculating the savings, however the actual savings will higher.

You also need to consider the ending balance, which would come out as follows:

2.69%   –   $424,797.47

2.79%   –   $425,635.09

The difference is $837.62, meaning this is how much less you will owe at the end of the 5 year term had you have taken the lower rate.

The difference on the payment comes to $1,515.60 as mentioned above, plus the $837.62 would then give you your total savings, right? 

Wrong.

This is there the next component comes into play.

Time Value of Money

The time value of money is a principle stating that money in your pocket at the present time will have a higher value than the same amount at a future date.  But why?

Money on its own has the capacity to earn interest.  With the lower rate option, that money kept aside can then be applied to other interest earning investments.  Even if you just choose to keep the additional money in your chequing account, the time value principle still applies, simply because you have it available.  If you do choose to keep in in a chequing account, then your money is depreciating since its actual value remains unchanged, however inflation continues, therefore decreasing its practical value over time.

In this case, the time value of money would be calculated using the higher mortgage rate option.  This would be calculated by using the payment from the higher rate on both options, and then calculating the difference between the ending balance.  This way you are comparing apples to apples.   

Again, the payment on 2.79% would be $2,312.68.  You would then use the same payment on the 2.69% option and then calculate the difference between the ending balance.

2.69% – $2,312.68 = ending balance of $423,177.80

2.79% – $2,312.68 = ending balance of $425,635.09

The difference between the two numbers is $2,457.29, which represents your true savings if you were apply the payment difference to your new mortgage.  If you choose to invest the difference and receive an after tax return that is higher than your mortgage rate you will come out further ahead.  Additionally, if you choose apply to difference to a credit card or other debt that has a rate higher than your mortgage rate you will come further out ahead.

Switching your mortgage to a lower rate mid-term

If rates are substantially lower than the rate you are paying, then it may make sense to convert your mortgage to a lower rate.  There are a few differences in the calculation:

Term length and amortization used for both options will be the time remaining on your current mortgage.

Penalty will be added to the balance on the lower rate option.

Let’s say you owe $500,000 on your mortgage and you are two years into a five year term at 3.29% with a monthly payment of $2,587.73.  You’ve confirmed with your lender that your penalty to break the mortgage early will be $6,000.   There is a new rate being offered at 2.54% and you want to see if it would make sense to switch.

Since there is three years remaining in the term, we would calculate the ending balance after three years (regardless of the fact that the new mortgage would be for a 5 year term).   As two years has passed, we would also lower the amortization to 23 years.

Up to $3,000 of the penalty can be capitalized into the new mortgage.  As the penalty in this case is $6,000, we would reduce the current amount owing by $3,000 (for calculation purposes only) since that portion is coming out of your pocket. This will compensate for its time value since it is an immediate expense.  The remaining $3,000 would be added to the new mortgage.

For this calculation, the current numbers look like this:

Mortgage amount owing:  $500,000 – $3,000 = $497,000

Current rate:  3.29%

Penalty $6,000

Payment $2,587.73

Balance at the end of term:  $450,378.29

The new mortgage would look like this:

New mortgage amount $500,000 + $3,000  = $503,000

New rate:   2.70%

Payment: $2,587.73

Balance at end of three years (current term end date): $445,892.09

$450,378.29 – $445,892.09 = $4,486.81 savings.

When comparing the two options, the difference in balance at the end of the current term is $4,486.81 in favour of switching to the lower rate.  As the penalty has already been added to the new mortgage, it has already been taken into consideration.  The $4,486.81 is what you would save, therefore switching mortgages is something that you may want to consider.

 

 

 

“Paul Meredith is the author of the Amazon #1 best selling book, Beat the Bank
– How to Win The Mortgage Game in Canada, and has ranked as one of the top
75 mortgage brokers in Canada since 2016. He was a finalist for Mortgage
Broker of the Year in 2018, and can be seen as the exclusive mortgage broker on
season two of TV’s Top Million Dollar Agent.”