# Does a cash back mortgage at a higher rate with the cash immediately applied to the principal make financial sense?

A mortgage advisor was trying to sell me on cash back mortgage. For most clients he said they use it to pay down debt at a higher interest rate or to buy the essentials for a first home. This is not my situation but he suggested it would make sense to take the 5% cash back and immediately apply it toward the principal. Doing this, even though the mortgage rate is 1% higher (3.79 instead of 2.79) at the end of the term the outstanding balance is smaller than it would be for the lower rate, if the payments were the same. Essentially he's pitching that it has a lower effective rate.

That last bit is where I question, because to get the payments the same he had to play around with the amortization period. I'm wondering if this is a gimmick others have encountered or is this a product which really is intended for a different use case but when applied this way it makes sense.

Update

Based on comments from @dwizum and @chris-degnen I have done a little more analysis. I think there may be one other important aspect to Canadian mortgages which I need to surface: The term of the mortgage and the amortization period are generally NOT the same. In the US you typically get a 30 year amortization mortgage that you could hold for 30 years. In Canada it is unusual, and usually costs significantly more to get a mortgage for a term of longer than 5 years. So part of the analysis here reflects knowing that a new mortgage will be required in 5 years.

Following the link that @chris-degnen shared explaining how semi-annually compounded mortgages in Canada are different than a typical US mortgage I used the Monthly Payment Mortgage Calculator - With Amortization Table spreadsheet to build out a comparison in a Google Sheet. I have shared the spreadsheet here.

The options are defined as follows:

Standard: This is a standard 25 year amortization mortgage at a fixed 2.79%

Standard Adj Amortization: Same as the Standard mortgage but the amortization period was artificially shortened to increase the payment to compare against others.

Standard + Prepayment: Same as the Standard but a monthly prepayment was added to increase the payment for comparison.

Cashback: The mortgage option driving this question, 5% cashback on the mortgage immediately applied and reducing the principal but also at a higher rate of 3.79% and still a standard 25 year amortization period.

Effective: This backs out the "effective rate" of the Cashback option.

Given that the mortgage will need to be renewed in 5 years the question becomes how much money is paid over the 5 year term and what is the balance on the mortgage. The lowest balance option should enable the smallest loan amount at renewal.

The Summary as per the initial Summary sheet is:

Standard: $277,521 paid and$851,270 remaining

Standard Adj Amortization: $293,395 paid and$834,263 remaining

Standard + Prepayment: $293,377 paid and$834,282 remaining

Cashback: $293,377.80 paid and$823,960 remaining

Effective: $293,377.80 paid and$823,960 remaining

There is a larger ($264) monthly payment for the Cashback over the Standard. But if that is acceptable the Cashback option works out to be most advantageous even over adding that same amount as a prepayment each month. As mentioned in the comments, if the mortgage is paid back early there is a penalty of paying back all/pro-rated 5% cashback. But if the mortgage is allowed to run to term then this is actually advantageous to pay 1% higher interest in exchange for the 5% in cash? • Per Chris's answer, we can't really be specific without knowing the rest of the details on the loan(s) you're being offered. Though, for a typical mortgage, it doesn't seem likely that a 5% discount on principal would be worth raising the interest rate by 1%. – dwizum Oct 10 '19 at 12:50 • "to get the payments the same he had to play around with the amortization period" This sounds fishy. Can he explain to you exactly how the period changes? Is it perhaps a bi-weekly payment instead of monthly? – D Stanley Oct 10 '19 at 14:10 • @dwizum I agree. I'm looking to create the same spreadsheet I was given with some round numbers to make it easier to follow and to remove the specifics of my personal situation. Then I can post specifics. – cclark Oct 10 '19 at 15:07 • @DStanley I agree and that is what caused me to ask. He said he was doing it to make the payments the same amount to show how the same monthly amount is paid at 2.79, 3.79 with the cash back and then that it was effectively a 2.57 rate. The payment frequency indeed remained the same at monthly. – cclark Oct 10 '19 at 15:08 • If you keep term the same, and your ultimate goal is the lowest total cost paid, comparing a 5% principal discount to a change in rate from 2.79 to 3.79 really only makes sense for very short mortgages (i.e. 10 years). Keeping the payment the same and playing with the amortization period (I'm assuming you mean term) is kind of a backwards way of selling this, so I also agree that it smells fishy. You can't come up with an "effective rate" for a principal discount without knowing the term, so it sounds like he just picked a term that made it seem like a good deal. – dwizum Oct 10 '19 at 15:21 ## 1 Answer Whether 5% cash back is an advantage depends on the figures. For example, for$1m over 10 years it is advantageous; over 15 years it is not.

Illustrating with calculations:

s is the principal
r is the monthly rate
n is the number of months
d is the monthly payment

s = 1000000
r = 2.79/100/12
n = 12*10 = 120
d = r s (1/((1 + r)^n - 1) + 1) = 9559.44


The balance b at month x is given by b:

x = n
b = (d + (1 + r)^x (r s - d))/r = 0


Apply cash back c, (not changing the rate yet):

c = s*0.05 = 50000
s = s - c = 950000


Now the balance in month x = 120 would be in credit:

b = (d + (1 + r)^x (r s - d))/r = -66068.97


(In fact, the loan would be repaid by month x = 114.)

Changing to the higher rate, the balance would still be in credit at x = 120:

r = 3.79/100/12
b = (d + (1 + r)^x (r s - d))/r = -5196.38


Now change the number of years to 15

s = 1000000
r = 2.79/100/12
n = 12*15 = 180
d = r s (1/((1 + r)^n - 1) + 1) = 6805.27

x = n
c = s*0.05 = 50000
s = s - c = 950000
r = 3.79/100/12
b = (d + (1 + r)^x (r s - d))/r = 29564.90


There is still a balance of \$29,564.90 to pay, so the cash back deal has not helped.

The loan would not actually be repaid until month 185, i.e. 15 years and 5 months.

x = 185
b = (d + (1 + r)^x (r s - d))/r = -4207.21


So the answer is, the deal can make financial sense, but it depends on the actual terms.

Edit

For Canadian mortgages, as described here, (with 2.79% substituted):

if you are quoted a rate of 2.79% on a mortgage, the mortgage will actually have an effective annual rate of 2.80946%, based on 1.395% semi-annually. However, you make your interest payments monthly, so your mortgage lender needs to use a monthly rate based on an annual rate that is less than 2.79%. Why? Because this rate will get compounded monthly. Therefore, we need to find the rate that compounded monthly, results in an effective annual rate of 2.80946%.

effective annual rate = (1 + 2.79/100/2)^2 - 1 = 0.0280946

monthly rate, r = (1 + 2.79/100/2)^(2/12) - 1 = 0.0023116


Running through the calculations again

For 10 years

s = 1000000
r = 0.0023116
n = 12*10 = 120
d = r s (1/((1 + r)^n - 1) + 1) = 9552.07

monthly rate, r = (1 + 3.79/100/2)^(2/12) - 1 = 0.00313368

x = n
c = s*0.05 = 50000
s = s - c = 950000
r = 0.00313368
b = (d + (1 + r)^x (r s - d))/r = -6045.71


For 15 years

s = 1000000
r = 0.0023116
n = 12*15 = 180
d = r s (1/((1 + r)^n - 1) + 1) = 6797.60

x = n
c = s*0.05 = 50000
s = s - c = 950000
r = 0.00313368
b = (d + (1 + r)^x (r s - d))/r = 27974.62


So with the Canadian system it doesn't make a great deal of difference.

• And most mortgages are 30 years. – RonJohn Oct 10 '19 at 13:46
• I did not include it in the original post but did tag the question as "Canada". That does change things slightly in that mortgage interest is compounded semi-annually and the term is usually 25 years although 30 year mortgages are available, usually at a higher rate. – cclark Oct 10 '19 at 15:15
• @cclark I have posted the calculations using the Canadian mortgage interest system. Again it shows that the mortgage term needs to be around 10 years for the deal to be advantageous. At 30 years it going to be quite disadvantageous. – Chris Degnen Oct 10 '19 at 15:52
• @ChrisDegnen I have edited the original question. I think there may be another subtlety of Canadian mortgages which comes into play here, the mortgage term and the amortization period are not the same as is common in the US. – cclark Oct 14 '19 at 19:03