The thinking behind weekly payments saving you money is this; If you pay $2,000 in monthly payments there are 30/31 days of interest charged before your next payment reduces your mortgage and therefore your interest. But if you split that same $2,000 into weekly instalments you are reducing your debt earlier and therefore paying less interest.
This is true but only in relation to the principal payment amount. Interest payments stay the same for the remaining mortgage whether paid monthly or split into weekly payments.
Not a lot.
As an example, at 2.5% interest, $2,000 of debt will incur $4.16 over a month. But paying that debt down in weekly instalments would mean only paying $2.40 worth of interest on that $2,000. A total savings of $1.76 for the month.
The benefit of weekly payments will increase fractionally over the life of your mortgage because your principal payments increase as your interest payments decrease, but this increase won’t be much. For a standard-sized mortgage over 30 years, weekly payments are unlikely to save you more than a few hundred dollars in total during that time.
People often assume paying weekly rather than monthly will have an ongoing compounded financial benefit. This is not the case. In the example above whether you pay weekly or monthly your mortgage is in the same financial position at the end of every month. Therefore the maximum you will ever save is that $1.76 per month. At the end of the day, you won’t be paying your mortgage down any faster.
Yes, it will because you have upped the payment amount by dividing a month into four weeks, equalling 48 payments over a year. In reality, you would be making 52 payments as per the calendar year. This will actually pay your mortgage off in 27 years not 30 years so is a great mind trick to use. But you could also just increase your monthly payments to $2,166 from $2,000 and achieve the same thing. The benefit isn’t from paying weekly, it’s from increasing your payments. Note that you would need to let the bank know your chosen weekly amount as the bank will otherwise automatically divide your annual payment by 52 to calculate your weekly payment.
Given the above, it is a personal call as to whether saving a couple of hundred dollars over the life of your mortgage is worthwhile enough to structure your principal payments to get this benefit.
A better option for many is to set up their mortgage payments to go out a day or so after payday. This helps people manage their money, thereby reducing cashflow anxiety a lot more than saving a handful of change in interest each month.
By far the best thing you can do to save money on your mortgage over the life of the loan is pay it off faster (here's an article on paying a good trick to pay down your mortgage sooner). Being clear on your budget is invaluable in determining whether or not you are able and willing to pay more of your principal off each month.
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