If I borrow 100k at 5% interest, and to be paid back in 5 years, why is it not that case that I just pay 21k per year and would have paid 105k after 5 years? I heard that if I pay back a little extra every year, it will help to go pay off the interest first, what does that mean? If I owe a set amount of money on fixed interest, how can the total amount change?
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Because 5% APR means that you’ll be paying 5% of the remaining principal per year. So in the first year, you owe 5k in interest, but near the end, you’ll owe much less in interest (so more goes towards the principal)
Interest rates are usually advertised as annual rates.
So, if you borrow $100,000 you owe $5000 interest the first year. So if you pay $21,000 in the first year, you’ve paid the $5000 in interest and $16,000 in principal. Now you have $84,000 left to pay and the interest for the second year will be $4200. Every year the interest goes down, so you are paying more principal and less interest. Any extra payments you make go directly principal so interest goes down as well.
In reality it’s a bit more complex since interest is calculated more often, maybe daily but it works out almost the same.
Mortgages use compound interest meaning in part that they charge interest on the amount owing on the loan, not the original amount.
Since your monthly payment is fixed this works out to you paying a greater percentage of interest and less principal at the start of the loan.
If you borrow $100,000 at 5% you’ll pay $5000 in interest in the first year
If your payment is $1000 a month, that’s $12000 of payments, or $7000 in principal paid off on the loan.
The following year you owe $93000 so you pay $4650 in interest and so on
The further along you are in the loan, the more principal you pay. So if you can over pay on your mortgage at the beginning and reduce your principal, it will greatly reduce how much you pay in interest in the long term.
(That’s not exactly how it works, interest is calculated by the payment not the year but you get the idea)
>If I borrow 100k at 5% interest, and to be paid back in 5 years, why is it not that case that I just pay 21k per year and would have paid 105k after 5 years?
That’s 5% interest per year not for the entire life of the loan
I think that this misunderstanding is the core of your questions.
When you let a mortgage just sit there (or any loan really) it will keep accruing interest over time.
It’s not a one and done flat fee for taking out the loan like you describe. With that in mind I’ll still answer some of your other questions.
>Why does a portion goes to interest and another to principle?
So that’s because of something called amortization. This means taking a loan and making it so that you pay the same amount of money every month on it .At the beginning of the loan you have a large outstanding loan that’s accruing interest.
(I’m mostly to slightly simplify the math here, btw but the concepts are all the same) With a 100k loan with 5% interest like you describe that means in the first year you will accrue 5k in interest. Now lets say your fixed payment is $900 a month
That’s about $400 a month in interest so for your early payments we be “paying off” about $400 a month in interest and the leftover amount, in this case $500, goes toward the principal. But let’s fast forward to when you only have 10k left on that loan. Now your interest is only about $40 a month. So $860 goes towards the principles.
>I heard that if I pay back a little extra every year, it will help to go pay off the interest first, what does that mean?
Simple, you spent less time with a large amount of money accruing interest. Let’s take a really extreme example. For that 100k loan after one year you might pay $5k interest that first year, and then about 4.9k in the second year, etc all the way to you paying a total of about 190k over 30 years
Or you can just pay off all the money immediately and pay zero interest at all.
>If I owe a set amount of money on fixed interest, how can the total amount change?
This goes back to that initial misunderstanding. Interest builds over time, it’s not a flat fee.
There are several types of mortgages. Some do work the way you think they should.
I’d like to preface this by saying it’s been about a decade since I went shopping for a mortgage, so some of these may not be used anymore.
You can indeed have the total amount calculated and just pay a fixed monthly amount. It wouldn’t be 105k in your example but something closer to 115/120k, since the interest listed is annual and not total. But the bank can do their fancy calculations and figure out you need to pay 24k (typically in monthly 2k payments) for 5 years to pay the full amount.
There’s also mortgages where you pay a set amount, but most of that payment goes to your interest. It’ll take a while before your payments start making a difference to the amount owed, but in the end nearly everything is paying off the loan and barely any interest remains. Those kinds of mortgages are mostly done for tax purposes (having a large debt is typically a write-off, so people keep the debt and pay the mortgage)
There’s also mortgages that consist of monthly payments+interest. So in your example, you’d pay something like 20k a year (again, monthly payments are typical) but also interest on top of that. So the first year you’d pay 25k total. Second year 24k, etc. It’s nice for people who want to lower their monthly expenses with time. Like young couples thinking of kids in a few years.
There’s probably more I haven’t mentioned, but these were the main three I was taught about a decade ago.
The ELI5 answer is that you pay interest on unpaid interest, which is significantly more than you might think.
A more detailed answer:
First, interest is usually a stated rate per year. So 100K borrowed at 5% per year would require a much larger payoff than 105K in five years. If the full amount of the loan is to be paid at the end of 5 years in one payment, it will be $127,628.16; this is different from the 105K payoff you hypothesized. The payoff can be calculated by the formula:
Future Value = Present Value * (1 + interest rate)^(Number of years)
Note: 5% is equivalent to the number 0.05
The present value is the borrowed amount and the future value is what you will pay back.
$127,628.16 = $100,000 * (1 + 0.05)^5
The reason this amount is different from the $105k you hypothesized is that you pay a fee (interest of 5% per year) on the money you owe and each year you owe a little more because you have not paid the interest that accumulates each year. At the end of the 5 year loan, you pay back your original debt (principal) and the sum of all the interest charges that have accumulated (interest). Essentially you owed interest on the unpaid interest that accumulated each year. That is what makes the whole system seem wonky. Please note that I am explaining the “simple” case where you borrowed money and made one payment at the end of the 5 year loan.
Mortgages are paid back in installments. There are two parts to your payments, the interest (the “fee” for borrowing) and the principal (what goes toward paying off your debt). With each payment some goes toward principal and then some goes to pay the interest on the outstanding debt. After a payment the next payment will have more going towards principal and less towards interest. The first payment will be almost 100% interest and the last payment will be almost 100% principal. Calculations for this are more detailed. I won’t get into them here…
In a somewhat idealized world, and from a borrowers perspective, if I want to make an extra payment on my mortgage I would like that to go directly towards my outstanding principal. That is the most effective way to lower the accumulated interest over the life of the loan and correspondingly the quickest way to pay off the loan. Why would I want to pay my bank interest (the fee for lending me money) early? I want to pay my principal early.
In practice, I have found that the only way my bank credits any extra payments towards principal is to conspicuously write “principal only” in the memo line of the check I write them. And then to call them after they “accidentally” credit my early payment towards interest I don’t owe yet, and insist they correct their mistake. After a few iterations of this they get the idea. Sort of a “they know, that I know, that they know” situation.
I took a class years and years ago that taught me this kind of stuff. The math is not hard and it changed the course of my life. They should teach it in high school.
The interest rate is the annual interest paid on the remaining balance. So you’d pay $5k in the first year, say $4k the second year (5% of the reduced principal), and lesser amounts of interest each subsequent year. The total of all the interest and principal is determined and them amortized to even the payment each month, with the interest vs. principal shifting over time.
> 5%
5% is the Annual Percentage Rate (APR). You only did 5% once, not each year, so 5 times (but each time there is less money owed, so less interest money), and also it’s broken up by 12 so it’s applied each month.
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Here’s a monthly payment formula:
**p•[(r/n)•(1+(r/n))^(n*t)]/[(1+(r/n))^(n*t)-1]**
[Here’s a WolframAlpha link so you can play around with the variables.](https://www.wolframalpha.com/input?i=p%E2%80%A2%5B%28r%2Fn%29%E2%80%A2%281%2B%28r%2Fn%29%29%5E%28n*t%29%5D%2F%5B%281%2B%28r%2Fn%29%29%5E%28n*t%29-1%5D++%3B+with+p+%3D+100000+%2C+r+%3D+0.05+%2C+n+%3D+12+%2C+t%3D5)
$1887.12, so around ~$113k paid back.
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> I heard that if I pay back a little extra every year, it will help to go pay off the interest first, what does that mean? If I owe a set amount of money on fixed interest, how can the total amount change?
Interest is on remaining amount of originally borrowed money owed (the principal, $100k), so if you can make extra payments towards principal, the remaining interest will be less. Your monthly payments will be the same (except the last month’s) but it will be paid back in less time.
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Also, don’t forget property taxes and insurance, usually bundled together in an escrow, so your monthly payment will be even more. My mortgage is $755/mo but the escrow is $360/mo, and my HOA is $315/mo.
The interest is usually annual, meaning that’s how much your debt grows every year. So $100k will grow to $105k, then $110,250 then $115,762.50, and so on. That is, if you don’t make any payments in the meantime. Usually loans require that you regularly make payments, and normally the payments are scheduled in such a way that you will pay off the loan in a certain period of time, say 10 years.
Now, the only way you can pay off a loan is if you pay more each year than you accumulate in interest. So for your $100k loan at 5%, you need to pay at least $5k the first year, otherwise you’ll be left with more debt than you started with. Now, of course you could compensate for that by paying more the next year, but usually the idea is that you start reducing your debt right away.
>I heard that if I pay back a little extra every year, it will help to go pay off the interest first, what does that mean?
Different loans may come with different terms but AFAIK this normally isn’t the case. Ultimately, there is just debt, and every payment goes towards reducing that debt, while interest is working to increase it. But it can be helpful sometimes to think about your payments as partly paying off interest and partly paying off the principal (i.e. the original sum you borrowed). And if you think about it that way, then it is true that you first pay off the interest, because as I said above, you have to pay the interest before you can make a dent in the principal.
However, assuming that your regular payments already pay off the annual interest (and more), then any *extra* payments you make will go completely towards the principal. For instance, let’s say you paid $500 per month for the first year, for a total of $6000. That leaves you with a debt of $99k: $5000 went into interest and the remaining $1000 towards the principal. Now at the end of the year, you decide you want to pay some more: an extra $4000. That brings the principal down to $95k.
The exception would be if the terms of your loan didn’t require (perhaps in the first years) that you pay off the annual interest in full each year. E.g. let’s say your required payments only amounted to $4k, then that would leave you with a debt of $101k at the end of the year, which is more than what you started with. In that scenario, any extra payment would first go towards killing that remaining $1k in interest.
(Such terms are more risky for the lender but also carry a greater potential reward for them, since the unpaid interest compounds year-on-year; 5% of 101k is more than 5% of 100k. But of course they also want you to pay them off in the end, so they don’t want this to go on forever.)
Your mortgage comes with preset duration, interest rate and monthly installments. The instalments are calculated in a way that if interest rate or duration doesn’t change, you’ll be able pay off the principal and interest completely in the agreed duration.
Since the interest is being accrued on a daily basis, paying some extra reduces the total payable by a little bit (doesn’t matter whether it’s principal or interest, as mortgage also includes interest on interest).
Paying a little extra every month helps reduce the amount payable and if you do it frequently enough, you can pay off the mortgage fairly quickly and with less overall interest.
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