What does a mortgage percentage rate really mean?

Question

I'm wondering if I could get a detailed explanation on exactly what a mortgage rate really means. For example, if you have a $250,000 mortgage, with a 25 year amortization, at 2.95%, with a 5 year term, then your payment would be about $1180. Over the 5 year term, the interest is about $34,200. So, how is that 2.95%? 2.95% of $250K is $7,500. $34,200 is about 13.7%! So, let's say you renew every 5 years for 25 years, at the same interest rate. In total, what would be the interest paid on the $250K. To me, it seems that the 2.95% is almost meaningless. Any mortgage experts care to elaborate?

Answer 1

The interest rate is the annualized interest rate you'll pay on the remaining principal balance each month. Since it's annualized, you'll divide the rate by 12, and pay 2.95%/12 = 0.24583% of the balance each month. For the first payment, your remaining principal is $250,000, and you'll pay 250,000 * 0.24583% = 614.58 in interest. The rest of the $1,180 goes to reducing the principal amount, so you'll pay slightly less interest in month 2, and so on until you're paying almost exclusively principal.

In the first year, you'll pay approximately 2.95% of the original principal ($7,375) in interest - it will be slightly less (actually $7,282) since your principal balance is going down each month.

$34,200 is about 13.7%

Sure, but that's interest paid over 5 years. If you average that, you're paying 13.7%/5 = 2.74%, which again is slightly less than the original 2.95% since the principal is going down over those 5 years.

In total, what would be the interest paid on the $250K

About $103,711, so the total amount paid over 25 years will be about $353,711

When you apply for a mortgage, you should receive an amortization schedule and other documents that clearly indicate how much you'll be paying in interest. If it isn't clear to you in the documents (and the closing company can't clarify it) then don't close on the mortgage. There are too many things that can be snuck in to a mortgage (variable rate, balloon payments, prepayment penalties) that can significantly change the amount you pay.

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EDIT

I just read the "5-year term" part. I'm assuming that means that there's a "balloon" payment due after 5 years. That changes part of the answer.

The loan is amortized as if you're paying it off over 25 years, but the term is only 5 years. At the end of 5 years (60 payments), you'll have reduced the principal to about $213,555. At that time, you'll need to pay that balance in full, either by just paying it outright or refinancing to a new loan. The risk you take is that interest rates will have risen between now and then, and your monthly payment could increase significantly. Unless you are certain that you'll move within 5 years (and thus would be paying off the loan anyways),I would avoid balloon payments and just go with a 25-year (or less) fixed rate mortgage.

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EDIT 2

The context of the question is Canadian mortgages, which work differently. I'm not an expert on Canadian mortgages, but here's what I've found out (which doesn't change the answer to the original question significantly):

Canadian mortgages are quotes using rates that compound semianually, (possibly to be equivalent to bonds). The actual interest rate would then be the semi-annual rate converted to a monthly rate by using the compound interest formula:

rm = (1 + ra/2)^(1/6)

So the monthly interest will be slightly less that the "annual" rate divided by 12. For the 2.95% rate in the original question, the monthly interest rate ends up being about 0.24434%, slightly less than the 0.24583% in the original answer. The fact that principal reduces, lowering the amount of interest that is paid over one year is still true - meaning you still don't pay 2.95% in interest over the year.