Prepaying a loan: Shouldn't the interest be recalculated like a shorter loan?

Question

Maybe I'm incorrect in my thinking, but I have a question about prepaying a loan. When you take out a mortgage on a home or a car loan, it is my understanding that for the first years of payment you are paying mostly interest.

So, let's take a mortgage loan that allows prepayment without penalty. If I have a 30 year mortgage and I have paid it for 15 years, by the 16th year almost all the interest on the 30 year loan has been paid to the bank and I'm only paying primarily principle for the remainder of the loan.

If suddenly I come into a large sum of money and decide I want to pay off the mortgage in the 16th year, but the bank has already received all the interest computed for 30 years, shouldn't the bank recompute the interest for 16 years and then recalculate what's actually owed in effect on a 16 year loan not a 30 year loan? It is my understanding that the bank doesn't do this. What they do is just tell you the balance owed under the 30 year agreement and that's your payoff amount.

That seems unfair. Shouldn't the loan be recalculated as a 16 year loan, which it actually has become? A few years ago I had a 5 year car loan. I wanted to prepay it after 2 years and I asked this question to the lender. I expected a reduction in the interest attached to the car loan since it didn't go the full 5 years. They basically told me I was crazy and the balance owed was the full amount of the 5 year car loan. I didn't prepay it because of this.

Answer 1

When you pay off a loan early, you pay the remaining principal, and you save all of the remaining interest. So you do save on interest, but it's the interest you would have paid in the future, not the interest you have paid in the past. (Your remaining balance when you pay off the loan only includes the principal, not the projected interest.)

Interest is a factor of the amount borrowed, the interest rate and the amount of time you borrow the money. The sooner you repay the money, the less interest you pay. Imagine if you had taken a 30 year loan at 4% interest but were allowed to make no payments until the loan term ended. If you waited 15 years to make your first payment, you wouldn't owe the same money as if you'd made payments every month. No, instead of owing ~$64k, you'd owe ~$182k, because you had borrowed $100k for 15 years (plus the interest due) rather than borrowing a declining sum.

So that's why you don't get a refund on interest for previous months. If you had started with a 16 year loan, then you would have been paying more principal every month, and your monthly amount due would have been higher to reflect that. As you paid the principal off faster, the interest each month would drop faster. Paying a huge portion of the principal at the end of the loan is not the same as steadily paying it down in the same time frame. You will pay a lot more interest in the former case, and rightfully so.

It might help to consider a credit card payment in comparison. If you run up a balance and pay only the minimum each month, you pay a lot of interest over time, because your principal goes down slowly. If you suddenly pay off your credit card, you don't have to pay any more interest, but you also don't get any interest back for previous months. That's because the interest accrued each month is based on your current balance, just like your mortgage. The minimum payments are calculated differently, but the interest accrued each month uses essentially the same mechanism.

Answer 2

One way to think of the typical fixed rate mortgage, is that you can calculate the balance at the end of the month. Add a month's interest (rate times balance, then divide by 12) then subtract your payment. The principal is now a bit less, and there's a snowball effect that continues to drop the principal more each month.

Even though some might object to my use of the word "compounding," a prepayment has that effect. e.g. you have a 5% mortgage, and pay $100 extra principal. If you did nothing else, 5% compounded over 28 years is about 4X. So, if you did this early on, it would reduce the last payment by about $400. Obviously, there are calculators and spreadsheets that can give the exact numbers.

I don't know the rules for car loans, but one would actually expect them to work similarly, and no, you are not crazy to expect that. Just the opposite.

Answer 3

A few years ago I had a 5 year car loan. I wanted to prepay it after 2 years and I asked this question to the lender. I expected a reduction in the interest attached to the car loan since it didn't go the full 5 years. They basically told me I was crazy and the balance owed was the full amount of the 5 year car loan.

This sounds like you either got a bad car loan (i.e. pay all the interest first before paying any principal), a crooked lender, or you were misunderstood. Most consumer loans (both car loans and mortgages) reduce the amount of interest you pay (not the _percentage) as you pay down principal. The amount of interest of each payment is computed by multiplying the balance owed by the periodic interest rate (e.g. if your loan is at 12% annual interest you'll pay 1% of the remaining principal each month).

Although that's the most common loan structure, there are others that are more complex and less friendly to the consumer. Typically those are used when credit is an issue and the lender wants to make sure they get as much interest up front as they can, and can recover the principal through a repossession or foreclosure.

It sounds like you got a precomputed interest loan. With these loans, the amount of interest you'd pay if you paid through the life of the loan is computed and added to the principal to get a total loan balance. You are required to pay back that entire amount, regardless of whether you pay early or not. You could still pay it early just to get that monkey off your back, but you may not save any interest. You are not crazy to think that you should be able to save on interest, though, as that's how normal loans work.

Next time you need to borrow money, make sure you understand the terms of the loan (and if you don't, ask someone else to help you). Or just save up cash and don't borrow money ;)

Answer 4

So, let's take a mortgage loan that allows prepayment without penalty. Say I have a 30 year mortgage and I have paid it for 15 years. By the 16th year almost all the interest on the 30 year loan has been paid to the bank

This is incorrect thinking. On a 30 year loan, at year 15 about 2/3's of the total interest to be paid has been paid, and the principal is about 1/3 lower than the original loan amount. You may want to play with some amortization calculators that are freely available to see this in action.

If you were to pay off the balance, at that point, you would avoid paying the remaining 1/3 of interest.

Consider a 100K 30 year mortgage at 4.5%

In month two the payment breaks down with $132 going to principal, and $374 going to interest. If, in month one, you had an extra $132 and directed it to principal, you would save $374 in interest. That is a great ROI and why it is wonderful to get out of debt as soon as possible.

The trouble with this is of course, is that most people can barely afford the mortgage payment when it is new so lets look at the same situation in year 15. Here, $271 would go to principal, and $235 to interest. So you would have to come up with more money to save less interest. It is still a great ROI, but less dramatic.

If you understand the "magic" of compounding interest, then you can understand loans. It is just compounding interest in reverse. It works against you.

Answer 5

Your thinking is unfortunately incorrect; an amortising loan (as opposed to interest only loans) pay down, or amortise, the principal with each payment. This means that the amount that is owed at prepayment will always be less than the total borrowed, and is also why some providers make a charge for prepayment. The "fairness" arguments that you make predicated on that misunderstanding are, therefore, incorrect.

Answer 6

Forget about terms. Think about loans in terms of months. To simplify things, let's consider a $1000 loan with .3% interest per month.

Month Principal Interest Payment
1     $1000     $3       $102
2      $901     $2.70    $102
3      $801.70  $2.41    $102
4      $702.11  $2.11    $102
5      $602.22  $1.81    $102
6      $502.03  $1.51    $102
7      $401.54  $1.20    $102
8      $300.74  $0.90    $102
9      $199.64  $0.60    $102
10      $98.24  $0.29     $98.53

This looks like a ten month term, but it's equally reasonable to think about it on a month-to-month basis. In the first month, you borrowed $1000 and accrued $3 interest. With the $102 payment, that leaves $901 which you borrow for another month. So on and so forth.

The payoff after five payments would by $503.54 ($502.03 principal plus $1.51 interest). You'd save $2.99 in interest after paying $13.54. The reason why most of the interest was already paid is that you already did most of the borrowing. You borrowed $502.03 for six months and about $100 each for five, four, three, two, and one month. So you borrowed about $4500 months (you borrowed $1000 for the first month, $901 for the second month, etc.). The total for a ten month $1000 loan is about $5500 months of borrowing. So you've done 9/11 of the borrowing. It's unsurprising that you've paid about 9/11 of the interest.

If you did this as a six month loan instead, then the payments look different. Say

Month Principal Interest Payment
1     $1000     $3       $169
2      $834     $2.54    $169
3      $667.54  $2.00    $169
4      $500.54  $1.50    $169
5      $333.04  $1.00    $169
6      $165.00  $0.50    $165.50

You borrow $1000 for one month. Then 834 for one month. So on and so forth. Adding that together, you get about $168.50 * 21 or $3538.50 months borrowed. Since you only borrow about 7/9 as much, you should pay 7/9 the interest. And if we adding things up, we get $10.54 in interest, about 7/9 of $13.54.

That's how I would expect your mortgage to work in the United States (and I'd expect it to be similar elsewhere). Mortgages are pretty straight-jacketed by federal and state regulations.

I too once had a car loan that claimed that early payment didn't matter. But to get rid of the loan, I made extra payments. And they ended up crediting me with an early release. In fact, they rebated part of my last payment. I saved several hundred dollars through the early release. Perhaps your loan did not work the same way. Perhaps it did. But in any case, mortgages don't generally work like you describe.

Answer 7

Loans do not carry an "interest balance". You can not pay off "all the interest". The only way to reduce the interest to zero is to pay off the loan.

Otherwise, the interest due each month is some percentage of the outstanding principal.

Think of it from the bank's perspective: they've invested some amount of money in you, and they expect a return on that investment in the form of interest. If you somehow paid in 16 years all the interest the bank expected to receive in 30 years, you've been scammed.

Answer 8

For the mortgage, you're confusing cause and effect.

Loans like mortgages generally have a very simple principle behind them: at any given time, the interest charged at that time is the product of the amount still owing and the interest rate. So for example on a mortgage of $100,000, at an interest rate of 5%, the interest charged for the first year would be $5,000. If you pay the interest plus another $20,000 after the first year, then in the second year the interest charge would be $4,000. This view is a bit of an over-simplification, but it gets the basic point across.

[In practice you would actually make payments through the year so the actual balance that interest is charged on would vary. Different mortgages would also treat compounding slightly differently, e.g. the interest might be added to the mortgage balance daily or monthly.]

So, it's natural that the interest charged on a mortgage reduces year-by-year as you pay off some of the mortgage. Mortgages are typically setup to have constant payments over the life of the mortgage (an "amortisation schedule"), calculated so that by the end of the planned mortgage term, you'll have paid off all of the principal. It's a straightforward effect of the way that interest works in general that these schedules incorporate higher interest payments early on in the mortgage, because that's the time when you owe more money.

If you go for a 15-year mortgage, each payment will involve you paying off significantly more principal each time than with a 30-year mortgage for the same balance - because with a 15-year mortgage, you need to hit 0 after 15 years, not 30. So since you pay off the principal faster, you naturally pay less interest even when you just compare the first 15 years.

In your case what you're talking about is paying off the mortgage using the 30-year payments for the first 15 years, and then suddenly paying off the remaining principal with a lump sum. But when you do that, overall you're still paying off principal later than if it had been a 15-year mortgage to begin with, so you should be charged more interest, because what you've done is not the same as having a 15-year mortgage.

You still will save the rest of the interest on the remaining 15 years of the term, unless there are pre-payment penalties.

For the car loan I'm not sure what is happening. Perhaps it's the same situation and you just misunderstood how it was explained. Or maybe it's setup with significant pre-payment penalties so you genuinely don't save anything by paying early.

Answer 9

There is no interest outstanding, per se. There is only principal outstanding. Initially, principal outstanding is simply your initial loan amount.

The first two sections discuss the math needed - just some arithmetic.

The One Important Formula

The interest that you owe is typically calculated on a monthly basis. The interested owed formula is simply (p*I)/12, where p is the principal outstanding, I is your annual interest, and you're dividing by 12 to turn annual to monthly.

What happens to Each Monthly Payment?

With a monthly payment, take out interest owed. What you have left gets applied into lowering your principal outstanding. If your actual monthly payment is less than the interest owed, then you have negative amortization where your principal outstanding goes up instead of down.

Regardless of how the monthly payment comes about (eg prepay, underpay, no payment), you just apply these two calculations above and you're set. The sections below will discuss these cases in differing payments in detail.

Fixed Monthly Payments

For a standard 30 year fixed rate loan, the monthly payment is calculated to pay-off the entire loan in 30 years. If you pay exactly this amount every month, your loan will be paid off, including the principal, in 30 years. The breakdown of the initial payment will be almost all interest, as you have noticed. Of course, there is a little bit of principal in that payment or your principal outstanding would not decrease and you would never pay off the loan.

Paying Less than the Required Monthly Payments

If you pay any amount less than the monthly payment, you extend the duration of your loan to longer than 30 years. How much less than the monthly payment will determine how much longer you extend your loan. If it's a little less, you may extend your loan to 40 years. It's possible to extend the loan to any duration you like by paying less. Mathematically, this makes sense, but legally, the loan department will say you're in breach of your contract.

Let's pay a little less and see what happens. If you pay exactly the interest owed = (p*I)/12, you would have an infinite duration loan where your principal outstanding would always be the same as your initial principal or the initial amount of your loan.

If you pay less than the interest owed, you will actually owe more every month. In other words, your principal outstanding will increase every month!!! This is called negative amortization. Of course, this includes the case where you make zero payment. You will owe more money every month.

Of course, for most loans, you cannot pay less than the required monthly payments. If you do, you are in default of the loan terms.

Paying More than the Required Monthly Payments (Prepay)

If you pay more than the required monthly payment, you shorten the duration of your loan. Your principal outstanding will be less by the amount that you overpaid the required monthly payment by. For example, if your required monthly payment is $200 and you paid $300, $100 will go into reducing your principal outstanding (in addition to the bit in the $200 used to pay down your principal outstanding). Of course, if you hit the lottery and overpay by the entire principal outstanding amount, then you will have paid off the entire loan in one shot!

Variable Monthly Payments

When you get to non-standard contracts, a loan can be structured to have any kind of required monthly payments. They don't have to be fixed.

For example, there are Balloon Loans where you have small monthly payments in the beginning and large monthly payments in the last year.

Is the math any different? Not really - you still apply the one important formula, interest owed = (p*I)/12, on a monthly basis. Then you break down the amount you paid for the month into the interest owed you just calculated and principal. You apply that principal amount to lowering your principal outstanding for the next month.

What happened with your 5 year car loan?

Supposing that what you have posted is accurate, the most likely scenario is that you have a structured 5 year car loan where your monthly payments are smaller than the required fixed monthly payment for a 5 year loan, so even after 2 years, you owe as much or more than you did in the beginning! That means you have some large balloon payments towards the end of your loan. All of this is just part of the contract and has nothing to do with your prepay.

Analyzing your Comments

Maybe I'm incorrect in my thinking, but I have a question about prepaying a loan. When you take out a mortgage on a home or a car loan, it is my understanding that for the first years of payment you are paying mostly interest.

Correct.

So, let's take a mortgage loan that allows prepayment without penalty. If I have a 30 year mortgage and I have paid it for 15 years, by the 16th year almost all the interest on the 30 year loan has been paid to the bank and I'm only paying primarily principle for the remainder of the loan.

Incorrect. It seems counter-intuitive, but even in year 16, about 53% of your monthly payment still goes to interest!!! It is hard to see this unless you try to do the calculations yourself in a spreadsheet.

If suddenly I come into a large sum of money and decide I want to pay off the mortgage in the 16th year, but the bank has already received all the interest computed for 30 years, shouldn't the bank recompute the interest for 16 years and then recalculate what's actually owed in effect on a 16 year loan not a 30 year loan? It is my understanding that the bank doesn't do this. What they do is just tell you the balance owed under the 30 year agreement and that's your payoff amount.

Your last sentence is correct. The payoff amount is simply the principal outstanding plus any interest from (p*I)/12 that you owe. In your example of trying to payoff the rest of your 30 year loan in year 16, you will owe around 68% of your original loan amount.

That seems unfair. Shouldn't the loan be recalculated as a 16 year loan, which it actually has become?

In fact, you do have the equivalent of a 15 year loan (30-15=15) at about 68% of your initial loan amount. If you refinanced, that's exactly what you would see. In other words, for a 30y loan at 5% for $10,000, you have monthly payments of $53.68, which is exactly the same as a 15y loan at 5% for $6,788.39 (your principal outstanding after 15 years of payments), which would also have monthly payments of $53.68.

A few years ago I had a 5 year car loan. I wanted to prepay it after 2 years and I asked this question to the lender. I expected a reduction in the interest attached to the car loan since it didn't go the full 5 years. They basically told me I was crazy and the balance owed was the full amount of the 5 year car loan. I didn't prepay it because of this.

That is the wrong reason for not prepaying. I suspect you have misunderstood the terms of the loan - look at the Variable Monthly Payments section above for a discussion.

The best thing to do with all loans is to read the terms carefully and do the calculations yourself in a spreadsheet. If you are able to get the cashflows spelled out in the contract, then you have understood the loan.

Answer 10

You are expecting, that if you pay off a 30 mortgage after 16 years, you should be charged the same amount of interest as someone who had a 16 year mortgage for the same amount and with the same interest rate.

This isn't correct, and here's why: the person with the 16 year mortgage paid it off faster than you. They paid more each month and the size of their loan shrunk faster than yours. After 15 years they had paid off a LOT more than you. You paid a lump sum after 16 years, but at this point, the extra money which they had paid had been in the banks hands for a long time. You caught up with them then, but you had been behind them for all of the previous years. On the other hand, you owed the same amount in each of those years as the person who took out a 30 year mortgage and didn't prepay. Therefore you paid the same amount of interest as this person, not the first person.

If you could arrange in advance a loan where you made the same payment as you did for 16 years, then paid the balance in a lump sum, then you would have paid exactly what you did.

Answer 11

If you take a loan, you make a contract with your lender, let's call them "bank" (even if it might not be a real bank). This loan contract contains an agreed-upon way of paying back the loan. Both sides agreed upon these conditions. Any change of it (like paying back early) needs the consent of both sides. So, in general, no, you cannot just pay back everything earlier unless the other side accepts this change of the contract.

Consider it from the bank's point of view: They want to earn money by getting the interest you have to pay when you pay back everything nice and slowly. It is their business. They plan on these expected revenues etc.

So if, for whatever reason, you have to pay back the whole remaining loan at once, you create a revenue loss for the bank and are liable for this financial damage. In German the term for this is "Vorfälligkeitsentschädigung" which translates to "prepayment penalty" or "acceleration fee". You just have to pay it, so in the end you come out like if you were paying back the loan in the agreed-upon fashion.

However, many loan contracts contain the option to pay back early at specific points in time in specific amounts and under specific conditions.

Answer 12

You seem to think that you are mostly paying interest in the first year because of the length of the loan period.

This is skipping a step. You are mostly paying interest in the first year because your principle (the amount you owe) is highest in the first year. You do pay down some principle in that first year; this reduces the principle in the second year, which in turn reduces the interest owed.

Your payments stay the same; so the amount you pay to principle goes up in that second year.

This continues year after year, and eventually you owe almost no interest, but are making the same payments, so almost all of your payment goes to principle.

It is a bit like "compounded interest", but it is "compounded principle reduction"; reducing your principle increases the rate you reduce it.

As you didn't reduce your principle until the 16th year, this has zero impact on the interest you owed in the first 15 years.

Now, for actual explicit numbers. You owe 100,000$ at 3% interest. You are paying your mortgage annually (keeps it simpler) and pay 5000$ per year.

Year      Principle Payment   Interest  Against Principle
0         100,000$  5,000$    3,000$    2,000$
1         98,000$   5,000$    2,940$    2,060$
2         95,940$   5,000$    2,878$    2,122$
3         93,818$   5,000$    2,815$    2,185$
4         91,633$   5,000$    2,749$    2,251$
5         89,382$   5,000$    2,681$    2,319$
6         87,063$   5,000$    2,612$    2,388$
7         84,675$   5,000$    2,540$    2,460$
8         82,215$   5,000$    2,466$    2,534$
9         79,682$   5,000$    2,390$    2,610$
10        77,072$   5,000$    2,312$    2,688$
11        74,384$   5,000$    2,232$    2,768$
12        71,616$   5,000$    2,148$    2,852$
13        68,764$   5,000$    2,063$    2,937$
14        65,827$   5,000$    1,975$    3,025$
15        62,802$   5,000$    1,884$    3,116$
16        59,686$   5,000$    1,791$    3,209$
17        56,477$   5,000$    1,694$    3,306$
18        53,171$   5,000$    1,595$    3,405$
19        49,766$   5,000$    1,493$    3,507$
20        46,259$   5,000$    1,388$    3,612$
21        42,647$   5,000$    1,279$    3,721$
22        38,926$   5,000$    1,168$    3,832$
23        35,094$   5,000$    1,053$    3,947$
24        31,147$   5,000$    934$      4,066$
25        27,081$   5,000$    812$      4,188$
26        22,894$   5,000$    687$      4,313$
27        18,581$   5,000$    557$      4,443$
28        14,138$   5,000$    424$      4,576$
29        9,562$    5,000$    287$      4,713$
30        4,849$    5,000$    145$      4,855$

The first year you put 3000$ against interest and 2000$ against principle.

By year 30, you put 145$ against interest and 4855$ against principle. because your principle was tiny, your interest was tiny.

Answer 13

The key to understanding a mortgage is to look at an amortization schedule. Put in 100k, 4.5% interest, 30 years, 360 monthly payments and look at the results. You should get roughly 507 monthly P&I payment. Amortization is only the loan portion, escrow for taxes and insurance and additional payments for PMI are extra.

You'll get a list of all the payments to match the numbers you enter. These won't exactly match what you really get in a mortgage, but they're close enough to demonstrate the way amortization works, and to plan a budget. For those terms, with equal monthly payments, you'll start paying 74% interest from the first payment. Each payment thereafter, that percentage drops.

The way this is all calculated is through the time value of money equations. https://en.wikipedia.org/wiki/Time_value_of_money. Read slowly, understand how the equations work, then look at the formula for Repeating Payment and Present Value. That is used to find the monthly payment.

You can validate that the formula works by using their answer and making a spreadsheet that has these columns: Previous balance, payment, interest, new balance. Each line represents a month. Calculate interest as previous balance * APR/12. Calculate new balance as previous balance minus payment plus interest.

Work through all this for a 1 year loan and you will understand a lot better.