My monthly mortgage payment is GBP965. Of that, monthly interest varies from GBP714 to GBP770. The annual interest rate 5.64% and the remaining term is just under 27 years, five years fixed.
Clearly the interest is currently much more than 5.64%. What’s the calculation here?
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The amount you pay in interest isn’t *quite* as simple as simply multiplying the remaining principal by the interest rate. There’s more steps to it because loans will have both an annual percentage rate (APR) and a compound rate. The compound rate is the APR divided by how often that fractional interest rate compounds with the year, and you have to consider *both*.
For example, let’s say we have two $100,000 loans each with an APR of 12%. One has a yearly compound rate, and one has a a monthly compound rate. So what we’re looking for here is a different APY, or annual percentage *yield*.
The formula for APY, when R is the APR and N is the number of times interest compounds in a year is APY = (1+r/n)^n – 1. Now we don’t have to worry about this math too much other than to realize as N gets bigger the APY gets bigger.
High level math, a $100,000 loan with a 12% APR and a 1 year compound period will, after 1 year, rise to $112,000.
But for a monthly compound period that figure is $112,682. The mere fact that interest is compounding monthly, instead of yearly *even though both initial loan amounts and both annual percentage rates are identical* makes a difference of $682.
As for why your rate varies month to month, I”m guessing the compound rate is “daily” (meaning *each and every day* the loan value increases by .0564/365 in interest) but you’re billed monthly, and some months have more days than others.
EDIT: that explains why your interest changes month to month but not why the payment stays the same. Put simply, banks already factor this in. They know the loan duration. They know the interest rate. They know how often that rate compounds, they know how often you make payments. Banks use a process called “amortization” to figure out *exactly* what your monthly payment should be, each and every month so that you pay it off exactly on time. That’s why fluctuations in how much you pay in interest every month don’t change your monthly payment. Your monthly payment has been calculated to factor all this in.
This used to be a manual process back in the day, there’s a whole set of complex formulas that go into it. Now there’s computer programs where you just plug in the various values and it instantly does the calculation.
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