I don’t seem to understand something regarding how interest is paid on a mortgage. Say the loan is for $100,000 at a 5% rate for 10 years, paid monthly.
I would think that on the first month, the interest I have to pay $100,000 × (0.05 ÷ 12) = $416.67. However the mortgage calculator says that the first payment is actually $412.39. While it’s not a huge difference, it’s a difference nonetheless and I can’t really figure out where it comes from.
My intuition is that it’s somehow related to the fact that interest is compounded daily, but when I take r = 0.05 ÷ 365 and N = 365 × 10 payments (keeping leap years in mind for later), and calculate the first 30 days, I get $409.70, and the first 31 days give $423.32. I guess that the “actual” number is some kind of weighted average since the calculator doesn’t ask at which month your loan starts.
So where is this $412.39 coming from? In reality when paying a mortgage, do you see the interest fluctuating as it decreases, depending on the number of days every month?
You need to figure out how many days there were in the first month calculation.
This page walks through the math to derive a Canadian mortgage cost:
https://www.mikesukmanowsky.com/blog/a-guide-to-canadian-mortgage-calculations
Apparently im Canada, mortgage interest may compound semi-annually, which might explain the difference.
Using the math on that page, I derived a monthly interest rate of 0.0041239 on your example loan. When multiplied by the principal of $100,000 I got a first-month interest fee of $412.39
Ah, that is the answer! 🙏
Indeed, it was the semi-annual compounding and effective interest rate that threw me off.
I can’t promise this is how the original site is calculating it, but I get exactly $412.39 of interest when I use half-yearly compounding: