# Amortization for an idiot

May 3, 2023 5:55 AM Subscribe

My ARM mortgage is resetting and the bank is also reamortizing the loan. Help me understand the math.

We overpay our mortgage every month by paying the same flat dollar amount that is something like 125% of the required payment. The mortgage has a 5 year adjustment feature and will soon adjust with a substantial increase in the interest rate - it is going up the full 2% allowed, from roughly 3% to 5%. So the interest is close to doubling. The bank is also reamortizing the loan over the remaining 25 years. I understand the interest increase, but the reamortization confuses me. The required monthly payment is going way down because of our prepayments. But the interest component of the required payment is going way up, as a proportion and as a dollar amount. We will keep making the same flat dollar payment, which will now be more like 175% of the new monthly requirement. Here is my question: ignoring the interest rate change, does the reamortization help me, hurt me, or do nothing? I suspect it does nothing, but perhaps it helps in the sense that prepaid principal is “taken off the back end” of a loan, which I vaguely think is disadvantageous to me because of the time value of money, but reamortization spreads out the prepayment across all months, including near term months. But in general I basically failed this part of math class.

We overpay our mortgage every month by paying the same flat dollar amount that is something like 125% of the required payment. The mortgage has a 5 year adjustment feature and will soon adjust with a substantial increase in the interest rate - it is going up the full 2% allowed, from roughly 3% to 5%. So the interest is close to doubling. The bank is also reamortizing the loan over the remaining 25 years. I understand the interest increase, but the reamortization confuses me. The required monthly payment is going way down because of our prepayments. But the interest component of the required payment is going way up, as a proportion and as a dollar amount. We will keep making the same flat dollar payment, which will now be more like 175% of the new monthly requirement. Here is my question: ignoring the interest rate change, does the reamortization help me, hurt me, or do nothing? I suspect it does nothing, but perhaps it helps in the sense that prepaid principal is “taken off the back end” of a loan, which I vaguely think is disadvantageous to me because of the time value of money, but reamortization spreads out the prepayment across all months, including near term months. But in general I basically failed this part of math class.

A mortgage has a principal amount, an interest rate, a monthly payment, and a term. If you have three of these, you can solve for the fourth.

When the bank does its calculation, it assumes the term is 25 years (300 months) and the interest rate and principal amount are known. When you make a larger monthly payment, the result is the length of time the mortgage takes to pay off (the term) is less.

The bank is resetting the term to 25 years. It calculates a new minimum payment you need to make. From the bank's point of view, it's selling a standardized product and telling the borrower the lowest monthly payment is it willing to accept on the loan. In terms of the calculation, the effect of the interest rate increase is not enough to offset the now lower principal amount, so the minimum monthly payment becomes lower.

If you continue to make the same payment, the length of time to pay off the mortgage with a higher interest rate will be longer than with the lower rate, but not as long as 25 years. The relationship of your actual payment to the new minimum payment is a bit of red herring.

posted by TORunner at 6:36 AM on May 3, 2023 [3 favorites]

When the bank does its calculation, it assumes the term is 25 years (300 months) and the interest rate and principal amount are known. When you make a larger monthly payment, the result is the length of time the mortgage takes to pay off (the term) is less.

The bank is resetting the term to 25 years. It calculates a new minimum payment you need to make. From the bank's point of view, it's selling a standardized product and telling the borrower the lowest monthly payment is it willing to accept on the loan. In terms of the calculation, the effect of the interest rate increase is not enough to offset the now lower principal amount, so the minimum monthly payment becomes lower.

If you continue to make the same payment, the length of time to pay off the mortgage with a higher interest rate will be longer than with the lower rate, but not as long as 25 years. The relationship of your actual payment to the new minimum payment is a bit of red herring.

posted by TORunner at 6:36 AM on May 3, 2023 [3 favorites]

I'll add that in my answer, when I say term, I'm talking about the mortgage term, not the interest rate term. The interest rate term doesn't affect the calculation being done here.

posted by TORunner at 6:41 AM on May 3, 2023

posted by TORunner at 6:41 AM on May 3, 2023

*does the reamortization help me, hurt me, or do nothing?*

It's not so much a question of helping vs hurting, but sound vs unsound financial planning relative to your circumstances

If you can afford the higher monthly payment that comes with a shorter amortization schedule than 25 years, going to the longer schedule would be financially unsound because a larger proportion of your monthly payment would be going to pay off interest charges rather than paying off principle. In the short run you'll be feeling the pain of higher monthly payments, but if you can suck it up and make do until interest rates go back down, you're going to save money over the life of your mortgage.

If you can't afford the higher monthly payment that comes with a shorter amortization schedule, then the 25-year schedule becomes you, because it attenuates the immediate "price shock" of interest rates more than doubling. You're going to pay a shit load more interest until interest rates settle and you can refinance, but you're monthly payments will be lower compared to the shorter amor schedule

There's really no right or wrong here

posted by BadgerDoctor at 7:05 AM on May 3, 2023

With the caveat that I am only familiar with Canadian mortgages, we saved a substantial amount when we were renegotiating our mortgage. It was originally a 5-year term amortized over 25 years and when we went in to reset the term, I mentioned the monthly amount we wanted to pay.

The mortgage salesperson* plugged in that amount and our principal and came up with a 5 year term and a 12-year amortization period with no penalty to switch, which we immediately signed. It helped us pay the house off faster. However, it did fix our payments to that amount.

Unlike your case, we had a limit to the amount we could pre-pay, so it made a

* She was let go a few weeks later, hopefully not related but...that math was not in favour of the bank.

posted by warriorqueen at 7:31 AM on May 3, 2023

The mortgage salesperson* plugged in that amount and our principal and came up with a 5 year term and a 12-year amortization period with no penalty to switch, which we immediately signed. It helped us pay the house off faster. However, it did fix our payments to that amount.

Unlike your case, we had a limit to the amount we could pre-pay, so it made a

*really*big difference for us.* She was let go a few weeks later, hopefully not related but...that math was not in favour of the bank.

posted by warriorqueen at 7:31 AM on May 3, 2023

Look at any amortization table and you will see that at the start your payment is almost all interest and very little principal. At the end, your payment is almost all principal and very little interest.

When you overpay, all of the extra payment goes to principal. This shortens the remaining time to pay back that loan.

At the five year interest rate reset, they reamortuze using the remaining 25 years and the amount of remaining principal. That principal is less than what was foreseen by the original amortization, because of your extra payments. But it is still 25 years. Hence the lower required payments.

Because it is a new amortization schedule, the required payments are initially almost all interest. But anything beyond the required payment goes directly to laying down the principal.

Tldr, you’re doing great. Just keep doing it and you’ll be fine.

posted by Winnie the Proust at 8:20 AM on May 3, 2023 [3 favorites]

When you overpay, all of the extra payment goes to principal. This shortens the remaining time to pay back that loan.

At the five year interest rate reset, they reamortuze using the remaining 25 years and the amount of remaining principal. That principal is less than what was foreseen by the original amortization, because of your extra payments. But it is still 25 years. Hence the lower required payments.

Because it is a new amortization schedule, the required payments are initially almost all interest. But anything beyond the required payment goes directly to laying down the principal.

Tldr, you’re doing great. Just keep doing it and you’ll be fine.

posted by Winnie the Proust at 8:20 AM on May 3, 2023 [3 favorites]

*does the reamortization help me, hurt me, or do nothing*

The term for this is recasting.

Because you're paying down your mortgage more than the minimum payment, it helps you. By driving down your principal with the extra payments, every time the mortgage is recast (usually yearly), it makes every subsequent payment (assuming you pay the same dollar amount rather than the minimum) more effective.

If you were to pay just the minimum after recasting, it would probably hurt you in the long run, given that interest rates are much higher now (and will probably stay higher) than if you'd gotten a fixed rate mortgage.

But with paying above the minimum, this can work out for you. Assuming interest rates don't skyrocket (unlikely), every time your mortgage is recast, your minimum payments will drop and your additional principal payments will become more effective, leading to a snowball effect.

If you itemize your deductions, don't forget that mortgage interest payments are deductible, which makes the math harder but benefits you if you do.

*But the interest component of the required payment is going way up, as a proportion and as a dollar amount.*

That's because interest rates have more than doubled. That's the risk of an ARM loan.

(In case it seems like I'm criticizing you, I'm in the same boat.)

posted by Candleman at 8:50 AM on May 3, 2023

You're not an idiot. Compounding interest is one of those things where intuition can fail spectacularly. If you don't mind the answer being off by a couple of bucks here or there, you can ballpark an amortization by thinking about years instead of getting hung up in 360 monthly payments.

SO! Let's say your original loan was ~$300,000. Your original rate was around 3%, and it sounds like it was a 30yr (2018-2047, say) loan. Round numbers, you pay ~$15,300/year (~$1,275/mo) to cover interest and pay down the principal to 0 at the end of 2047 (year 30). (doing the math at a monthly scale changes that a little bit, but it's close.)

So you paid 125% of that amount (call it $1,600/month?) for 5 years. Great! I'm assuming your bank didn't give you the runaround where they take the overage and park it somewhere----either you explicitly told them to apply the extra 25% to principal, or they're doing that automatically, but it went against principal. So after paying 125% of your monthly payment for 5 years, your principal is something like $246,000. Is that about right? (Around 82% of your original principal still remains?)

Because if I put a $246,000 loan with 25 years into a loan calculator at 5%, it tells me that the required monthly payment is closer to $1,450 than $1,275... which means your $1,600/month is close to 10% higher than the minimum payment than 75% higher. Maybe the terms of the amortization are different than just "assume 25 years to pay off the $246,000 at 5%."

Round numbers---3% of $300,000 is $9,000, so you're paying on the order of

posted by adekllny at 9:01 AM on May 3, 2023

SO! Let's say your original loan was ~$300,000. Your original rate was around 3%, and it sounds like it was a 30yr (2018-2047, say) loan. Round numbers, you pay ~$15,300/year (~$1,275/mo) to cover interest and pay down the principal to 0 at the end of 2047 (year 30). (doing the math at a monthly scale changes that a little bit, but it's close.)

So you paid 125% of that amount (call it $1,600/month?) for 5 years. Great! I'm assuming your bank didn't give you the runaround where they take the overage and park it somewhere----either you explicitly told them to apply the extra 25% to principal, or they're doing that automatically, but it went against principal. So after paying 125% of your monthly payment for 5 years, your principal is something like $246,000. Is that about right? (Around 82% of your original principal still remains?)

Because if I put a $246,000 loan with 25 years into a loan calculator at 5%, it tells me that the required monthly payment is closer to $1,450 than $1,275... which means your $1,600/month is close to 10% higher than the minimum payment than 75% higher. Maybe the terms of the amortization are different than just "assume 25 years to pay off the $246,000 at 5%."

Round numbers---3% of $300,000 is $9,000, so you're paying on the order of

**$9,000/year**in interest for the first couple years. If your balance comes down to ~$240,000**but**your rate goes up to 5%, the interest you're paying for the next couple years comes out to**~$12,000/year**. So there's $250/month of your payment that serves that extra $3,000 annually in interest starting with the new rate. Long story short, I'm comfortable with the math and I'm confused too. If your original numbers are close-to-right, I either misunderstand something about your loan terms or I messed up the math.posted by adekllny at 9:01 AM on May 3, 2023

In a way, it helps.

Since they're reamortised it, they've spread the remaining principal payments over a longer period, and as you note that's a lower monthly payment. Think of that as what they

In the current situation where you're overpaying, you're paying the principal at the speed you choose to pay it (that is, faster). The amortisation schedule doesn't change anything about this because you're effectively ignoring it. So it changes nothing - you keep overpaying and you'll pay off the mortgage early, same as before. (Confirm there are no overpayment or early termination penalties, just to be safe.)

The reamortisation also doesn't change the speed you're paying off the mortgage - you may be paying 175% of what they insist you pay, now, but you'll be paying a similar amount of principal each month as you were before - slightly less because there's more interest to pay, but in the same ballpark. They don't

As someone said above, see if they will offer you a lower rate for a shorter term. They might not, or they might charge you a lot of money to switch, so you might choose not to change. If they do, then you're committing to a higher minimum payment, but in return you save on interest payments. (Given that your rate rise is limited, your current 5% rate is probably cheaper than the market would get you, though.)

posted by How much is that froggie in the window at 9:13 AM on May 3, 2023

Since they're reamortised it, they've spread the remaining principal payments over a longer period, and as you note that's a lower monthly payment. Think of that as what they

*require*you to pay each month. In the worst case, if your finances get tight, you don't need to pay as much of the mortgage off each month. Obviously, if you do that you'll ultimately pay for the slow payments in more interest later, but it's an option that's available to you in tight times (versus now, where you have to pay more to keep on top of it because they require a higher principal payment from you).In the current situation where you're overpaying, you're paying the principal at the speed you choose to pay it (that is, faster). The amortisation schedule doesn't change anything about this because you're effectively ignoring it. So it changes nothing - you keep overpaying and you'll pay off the mortgage early, same as before. (Confirm there are no overpayment or early termination penalties, just to be safe.)

The reamortisation also doesn't change the speed you're paying off the mortgage - you may be paying 175% of what they insist you pay, now, but you'll be paying a similar amount of principal each month as you were before - slightly less because there's more interest to pay, but in the same ballpark. They don't

*require*you to pay as much principal as they did before, so that's proportionally a lot more than they*require*, now, but in absolute terms it's about the same.As someone said above, see if they will offer you a lower rate for a shorter term. They might not, or they might charge you a lot of money to switch, so you might choose not to change. If they do, then you're committing to a higher minimum payment, but in return you save on interest payments. (Given that your rate rise is limited, your current 5% rate is probably cheaper than the market would get you, though.)

posted by How much is that froggie in the window at 9:13 AM on May 3, 2023

Response by poster: Adekllny - I was afraid someone was going to do that! The 125% and 175% figures in my OP were really just plug numbers - we have made some one-time additional paydowns that mess up the math - the main point is that we always pay the same monthly amount, that amount was X% higher than required before reamortization, and will now be X%+[a significant part more] higher than required after reamortization. I am really just trying to understand conceptually if reamortization matters, setting aside the change in interest rates. I.e., I now pay the same $Z that I have always paid per month, but more of that is getting consumed in interest because more of the required payment is allocated to interest (again, setting aside the 2% increase, the portion of the required payment dedicated to interest is higher than before).

posted by Mid at 9:24 AM on May 3, 2023 [1 favorite]

posted by Mid at 9:24 AM on May 3, 2023 [1 favorite]

*I am really just trying to understand conceptually if reamortization matters, setting aside the change in interest rates.*

Per above, it does when paying down principal above the minimum payment. You can play with this with mortgage amortization tools that allow for calculating additional principal payments.

Every time your loan is recast (again, assuming US rules), the calculations are essentially as if you got a new loan with N-1 years on it. So if you're on year 25 and have reduced the principal to $200,000, you can put $200K into the calculator for a 24 year loan and see what your new balance between interest and principal will be. Then do the same thing with your estimated principal with a 23 year loan based on what extra you think you'll be able to pay off this year. And so on.

posted by Candleman at 12:48 PM on May 3, 2023 [1 favorite]

*I am really just trying to understand conceptually if reamortization matters*

If I'm understanding you correctly with some fake numbers:

Your mortgage payment had been $2000, but you'd been consistently paying $2200. Your interest rate has gone up but they recast the mortgage so now your mortgage payment is $1800 and you intend to keep paying $2200, with excess going to principal.

Then it doesn't matter. Again with fake numbers:

Month 1: You owe $300,000, so you've borrowed $300,000 for a month and owe $1250 in interest. The mortgage being recast doesn't change this. You also pay $950 in principal, well over what they ask you to pay. The mortgage recast doesn't affect this either.

Month 2: You've borrowed $299050 and owe about $1246 in interest, and the recast doesn't change this. You pay $954 in principal, well in excess of what they ask, and the recast doesn't affect this.

Repeat for remaining months. Every month you owe $X based on how much money you borrowed that month, and every month you pay at least $950 in principal. The only thing the recast affects is how much you *have to* pay on your mortgage if you go bonkers four Christmases from now and don't wanna pay your extra bit.

posted by GCU Sweet and Full of Grace at 2:42 PM on May 3, 2023 [2 favorites]

I agree with GCU. Pretty sure Candleman's most recent answer is either missing a "not" in "then it does [matter]," or he's thinking of excess payments as a fixed amount above the (new vs old) minimum instead of -- as in the original question -- a fixed total amount being sent in each month regardless of the new minimum.

For the asker, the key piece of information you might be missing is that at the beginning of a mortgage (or right after a recasting), there's no hand-on-the-scale that's making more of the early payments go toward interest. You're only ever paying the amount of interest that's actually been accrued that month, and that number just naturally goes down over time as the principal gets smaller.

(And a greater

posted by nobody at 5:22 AM on May 4, 2023 [1 favorite]

For the asker, the key piece of information you might be missing is that at the beginning of a mortgage (or right after a recasting), there's no hand-on-the-scale that's making more of the early payments go toward interest. You're only ever paying the amount of interest that's actually been accrued that month, and that number just naturally goes down over time as the principal gets smaller.

(And a greater

*percentage*of a post-recasting-with-no-rate-hike minimum payment would go toward interest only because the minimum payment has been made smaller, not because the amount going toward interest has been made artificially greater. In the theoretical absence of a rate hike -- and assuming you're still making the same payments regardless of the new minimum -- the dollar amount going toward interest wouldn't have changed pre- and post-recasting.)posted by nobody at 5:22 AM on May 4, 2023 [1 favorite]

*I agree with GCU. Pretty sure Candleman's most recent answer is either missing a "not" in "then it does [matter]," or he's thinking of excess payments as a fixed amount above the (new vs old) minimum instead of -- as in the original question -- a fixed total amount being sent in each month regardless of the new minimum.*

No, there's not a missing not and it doesn't matter if the excess payments are a fixed amount or can fluctuate. I can put an extra $1 into an account that's getting recast compared to one that's not and it will still have a ripple effect.

If you're paying down the principal above the minimum payment, every time the loan is recast, your new minimum payment goes down and the efficacy of your payments goes up, relative to what your payment would be if you weren't paying down the principal. Depending on interest rates with an ARM, your minimum payment may exceed the previous year's, but with paying down the principal, recasting always works in the borrower's favor (although investing the same amount of money in a higher performing investment may still be better).

This is easy to see - go to an amortization calculator and create a 30 year loan with and without an extra $100/month payment. Then create a 29 year loan (which is basically what recasting is) based on the principal left after a year from both options. You'll see that even without continuing additional principal payments, that every payment in the version where you paid an extra $100/month for the first year has more of an effect. The required minimum will go down but if you continue paying what you would have owed, you get a snowball effect.

Paying down a loan that is being recast yearly will always benefit a consumer compared to not doing so, but investing the same money in alternative investments (including but not limited to the S&P 500 or Nasdaq) can outperform it. In the days of ultralow interest (e.g. 2018-2022) it made sense to do so. These days, maybe not so much.

posted by Candleman at 6:06 PM on May 4, 2023

Correction - in the days of very low interest rates and high performing stocks, it made sense to invest in the stock market while not paying down low interest rate ARMs, but these days the situation may be reversed.

posted by Candleman at 6:16 PM on May 4, 2023

posted by Candleman at 6:16 PM on May 4, 2023

I do think you're missing something here, Candleman -- or maybe just answering a question slightly different than the one asked. (Or correct me if I'm making a mistake with my numbers?)

Amortization calculator showing a 200k mortgage at 6% for 30 years, with an extra payment of $100 made each month. [Note the 1,199.10 minimum payment + 100 = 1299.10 total, which doesn't get displayed on that page anywhere.]

Amortization calculator for a $150,983.52 mortgage [the balance remaining in the above example at the end of year 10], at 6% for the 20 remaining years with an extra payment of $217.41 made each month. [217.41 because the new $1,081.69 minimum payment is 217.41 less than the 1299.10 they were sending in each month before.]

Comparing the yearly ending balances for the second example with the equivalent (year+10) from the first, I'm only seeing rounding errors of pennies' difference.

(Just in case, I reran this with a larger $500 extra monthly payment for the first 10 years -- which became 1,087.04 after the recasting to make the total monthly payments the same this time -- and I'm still seeing only pennies' difference, this time in the opposite direction: Before recasting and after recasting.)

These do all seem to show that the recasting itself has no meaningful effect in either direction on the amount of interest you're paying

posted by nobody at 11:54 PM on May 4, 2023

Amortization calculator showing a 200k mortgage at 6% for 30 years, with an extra payment of $100 made each month. [Note the 1,199.10 minimum payment + 100 = 1299.10 total, which doesn't get displayed on that page anywhere.]

Amortization calculator for a $150,983.52 mortgage [the balance remaining in the above example at the end of year 10], at 6% for the 20 remaining years with an extra payment of $217.41 made each month. [217.41 because the new $1,081.69 minimum payment is 217.41 less than the 1299.10 they were sending in each month before.]

Comparing the yearly ending balances for the second example with the equivalent (year+10) from the first, I'm only seeing rounding errors of pennies' difference.

(Just in case, I reran this with a larger $500 extra monthly payment for the first 10 years -- which became 1,087.04 after the recasting to make the total monthly payments the same this time -- and I'm still seeing only pennies' difference, this time in the opposite direction: Before recasting and after recasting.)

These do all seem to show that the recasting itself has no meaningful effect in either direction on the amount of interest you're paying

*as long as you keep sending in the same total amount each month*. (The recasting just lowers the minimum required monthly payment.)posted by nobody at 11:54 PM on May 4, 2023

Response by poster: I think this back-and-forth is exactly the issue that is/was confusing me!

posted by Mid at 6:29 AM on May 5, 2023

posted by Mid at 6:29 AM on May 5, 2023

Well, if it's any consolation, the most recent back-and-forth seems to be between whether the recasting is good or whether it's neutral for your situation, so either way at least you don't have to worry about it being a bad thing! (But it sure looks to me like it's neutral, in and of itself, at least as far as any potential extra interest cost is concerned. And a positive if you fall on hard times at some point and could use the temporary relief of the lower required monthly payments.)

posted by nobody at 11:11 AM on May 6, 2023 [1 favorite]

posted by nobody at 11:11 AM on May 6, 2023 [1 favorite]

*If you're paying down the principal above the minimum payment, every time the loan is recast, your new minimum payment goes down and the efficacy of your payments goes up*

That would be true if the line-item for "interest" on the bill for the 67th month was whatever was originally calculated to be the interest due during the 67th month. AFAIK this isn't true, though. AFAIK, the line-item that appears for the 67th month is (amount owed after the 66th month's payments) \times (interest rate / 12).

posted by GCU Sweet and Full of Grace at 10:04 AM on May 8, 2023

This thread is closed to new comments.

Basically, reamortizing means recalculating the monthly payment so that the principal hits zero at the end of the amortization period. If you keep paying the same dollar amount, the reamortization does nothing (assuming that the new terms do not include any new prepayment penalties or limits).

posted by heatherlogan at 6:27 AM on May 3, 2023 [1 favorite]