How are interest and monthly payments calculated on a 30 year fixed rate mortgage loan?
Suppose there is a 30 year loan of 500,000 at 8% interest.
Would that 8% interest have to be paid each year for whatever amount is still left? Ex. 8% of 500,000 is 40,000, so the first year we would have to pay 40,000 in interest, then the next year about be 8% of whatever principal is left, so if 20,000 went to principal we have 480,000 left on the loan and 8% of that is 38,400 paid in interest only the second year.
Or is it calculated differently.
Thanks!
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It will be calculated monthly. This is why paying even a little extra each month can make a big difference over the term of the loan.
The best way to look at it is this.
Mortgage payments have two parts. The principal and the interest.
The principal is the loan itself and the interest is the fee the lender charges. So let’s say you have a loan amount of 200,000 with an interest rate of 6%. You are making monthly payments. So you would use this calculation.
6% = .06
So take .06 and divide by 12 since we are making monthly payments.
.06 / 12 = .005
take .005 and multiply it by the remaining principal of the loan.
.005 * 200000 = 1000
So your first months interest ould be $1000
1/12th of the interest rate is applied each month because the 8% rate is **per year** and there are 12 months in a year.
For example, in the first month $500,000 x 8% x 1/12 = $3,333.33 in interest.
Your math is roughly correct.
if it’s 8% interest on a 500,000 loan, then 0.8% * 500,000 = $40,000 year 1. $40,000 / 12 months = $3,333 per month. So you’d pay that amount per month, in interest alone. Add to that principal, taxes, and insurance.
That is fuzzy math because it’s not counting that each month you reduce the principal slightly so in February the 8% is on a slightly smaller value than January’s was.
It’s “amortized” to be a simple interest calculation.
It’s the remaining balance, times by the APR (broken up monthly).
I had a $168k mortgage at 3.5%.
$168000 * (3.5%/12) = $490.00 of interest.
And checking my mortgage account, that’s exactly how much the interest was. The principal was $264.40, so the loan balance is lowered to only $16773.50, and the next month’s interest is calculated on that.
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To calculate the total fixed monthly (interest+principal) you need to use a formula:
* Principal * APR %/12 * (1+ APR %/12)^((number of months)) / [(1+APR %/12)^((number of months)) – 1]
For example for mine:
168000 * 0.035/12 * (1+ 0.035/12)^(360) / [(1+0.035/12)^(360) – 1] = $754.40
As stated, my first month’s interest was $490 and the principal was $264.40, which makes $754.50; each month the monthly stays the same but the interest portion decreases and the principal portion increases.
Yeah, that’s basically it… there is more interest early on, less down the road. The total amount of interest and principal are amortized so that the payments remain the same, but ratio of interest to principal shift over time.
It’s a rate of 8% per annum, calculated on whatever the outstanding loan balance is, but that balance changes over time. When you close the loan balance is $500K, but part of your first payment is applied to principal, which decreases the outstanding balance slightly. This is called amortization. Home loans generally use “mortgage style” amortization, in which a formula is used to determine a level/fixed monthly payment (which has both a principal and interest component) that will result in the full amortization of the initial loan balance over the 30 year term.
Each month, you are charged 1/12 of the interest rate based on your remaining principal balance that month. So let’s take your example of a $500k loan with 8% interest.
In month 1, your interest will be equal to 1/12th of 8% (or 2/3 of 1%) times $500,000, or $3333.33. In addition to that interest, you will pay some amount of principal as well ($335.49, to be exact, making your remaining principal balance $499,664.51), for a total monthly payment of $3668.82.
In month 2, your interest will be equal to 1/12th of 8% times your new principal balance ($499,664.51), or $3331.10. But your monthly payment doesn’t change thanks to a fancy thing called amortization, so that means that that month’s payment will have $2.23 less going toward your interest and $2.23 more going toward your principal.
In month 3, your interest is $2.25 less than it was in month 2, so your principal is getting paid down a little faster still. And so on, and so forth.
So at the end of year 1, you’re actually paying a total of $39,849.05 in interest, not $40,000 which you might expect from an 8% interest rate on a $500k balance, because the interest that you’re charged goes down a tiny bit each month as your mortgage is paid down. Over time, the balance between principal and interest will start to shift significantly, so much so that in year 30 of your mortgage, you’re paying less than $2000 in interest despite the fact that your total monthly payment isn’t changing at all.
If you look at an [Amortization Calculator](https://www.calculator.net/amortization-calculator.html?cloanamount=500%2C000&cloanterm=30&cloantermmonth=0&cinterestrate=8&cstartmonth=10&cstartyear=2023&cexma=0&cexmsm=10&cexmsy=2023&cexya=0&cexysm=10&cexysy=2023&cexoa=0&cexosm=10&cexosy=2023&caot=0&xa1=0&xm1=10&xy1=2023&xa2=0&xm2=10&xy2=2023&xa3=0&xm3=10&xy3=2023&xa4=0&xm4=10&xy4=2023&xa5=0&xm5=10&xy5=2023&xa6=0&xm6=10&xy6=2023&xa7=0&xm7=10&xy7=2023&xa8=0&xm8=10&xy8=2023&xa9=0&xm9=10&xy9=2023&xa10=0&xm10=10&xy10=2023&printit=0&x=Calculate#calresult), you can see this effect in action. Look for the “Monthly Schedule” link above the table on the left to see a month by month breakdown. Amortization helps keep your monthly payments affordable in the early years of your mortgage, at the expense of not making much headway on paying down your principal until the late years of the mortgage.
The math (from memory) is
Each month
Take the interest rate divided by 12 and that value is multiplied by the outstanding balance. This is how much interest you pay that month.
Since you also pay some principle next month the same calculation has you pay a little bit less interest.
The first month you pay 8%/12 (depending on the convention it could be 1/12 or [actual days in the month]/365 which is roughly 1/12 but varies from month to month). To keep it simple we’ll use the 1/12 convention in the numbers.
So, the first month the $500,000 note balance generates $3,333.33 in interest and the payment is going to be $3,668.82. Which means the next month the balance starts at this amount ($499,664.51). The next month the interest will be slightly less (because it’s now 8%/12 times the new balance) and the principal payment is slightly larger).
The idea is to give the borrower a constant payment that repays the entire loan after 360 payments or 30 years.
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