# Solving for mortgage payment amount and its deduction on the total principal?

This question is stumping me.

"Jane has taken out a 20-year, \$150,000 mortgage with monthly payments (made at the end of each month) at a stated mortgage rate of 6.8% per year compounded semi-annually. If she makes each payment on time, what will be the mortgage principal remaining after 10 years?"

How to approach this question and answer it? I've got a test and need to solve this by hand using a calculator.

It says 'stated mortgage rate': am I supposed to convert that to the effective annual rate?

• In the US, mortgage interest accrues each month. I've never heard of an amortized mortgage compounding semi-annually. Are you sure you read this correctly? – JTP - Apologise to Monica May 26 '14 at 23:51
• Yes, this is the question we were given. It's a hypothetical example for a university question in the course. I copied and pasted it. – Johnny May 27 '14 at 0:14
• This question appears to be off-topic because it is about homework. – littleadv May 27 '14 at 0:29
• @littleadv But... is homework off-topic? See Meta - Should homework questions be allowed? This kind of question would otherwise fit the site, wouldn't it? – Chris W. Rea May 27 '14 at 4:32
• @JoeTaxpayer Canadian mortgages compound semi-annually. – Chris W. Rea May 27 '14 at 4:52

I would suggest that you review the course material, but this is what I was able to find:

Unfortunately, mortgages are not as simple. With the exception of variable rate mortgages, all mortgages are compounded semi-annually, by law. Therefore, if you are quoted a rate of 6% on a mortgage, the mortgage will actually have an effective annual rate of 6.09%, based on 3% 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 6%. 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 6.09%. Mathematically, this would be:

((1+rM)^12)-1 = 0.0609

rM = (1.0609)^(1/12)

rM = 0.493862…%

Notice, that the annual equivalent of his rate is slightly less than 6%, at 5.926% (0.493862 x 12 = 5.926%). In other words, 5.926% compounded monthly is 6.09% annually. By the way, I recommend to my students learning this for my university courses that they use 8 decimals in their interest rate to assure that they can be accurate to the penny.

the original 0.0609 is (1.03*1.03 )-1