Does a home mortgage use Simple or Compund Interest?

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SavingCash
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Does a home mortgage use Simple or Compund Interest?

Post by SavingCash » Mon Aug 05, 2013 8:54 am

Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you

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JamesSFO
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Re: Does a home mortgage use Simple or Compund Interest?

Post by JamesSFO » Mon Aug 05, 2013 8:56 am

Google: mortgage simple or compound

Top links include mortgage professor with the answer:
Mortgages can also be simple interest or compound interest. However, all mortgages are simple interest except those involving negative amortization, where the payment does not cover the interest. (If unpaid interest is added to the balance, as it is on a negative amortization loan, in future months, interest is calculated on a balance that includes unpaid interest, which makes it a compound interest loan.) Absent negative amortization, all mortgages are simple interest.
URL: http://www.mtgprofessor.com/a%20-%20sim ... lature.htm

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dm200
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Re: Does a home mortgage use Simple or Compund Interest?

Post by dm200 » Mon Aug 05, 2013 9:46 am

JamesSFO wrote:Google: mortgage simple or compound

Top links include mortgage professor with the answer:
Mortgages can also be simple interest or compound interest. However, all mortgages are simple interest except those involving negative amortization, where the payment does not cover the interest. (If unpaid interest is added to the balance, as it is on a negative amortization loan, in future months, interest is calculated on a balance that includes unpaid interest, which makes it a compound interest loan.) Absent negative amortization, all mortgages are simple interest.
URL: http://www.mtgprofessor.com/a%20-%20sim ... lature.htm
While almost all US mortgages are simple interest, in almost all cases, mortgage loans do not charge "daily interest" as many or most consumer loans do. Most mortgages charge monthly interest, which is the same amount whether you make the monthly payment ten days early or just at the end of the grace period. On many consumer installment loans, if you make the monthly payment ten days early each month, you are charged less interest because the interest is charged on the outstanding principal on the loan each day.

So, in practical terms, it makes sense to pay the credit union installment auto loan payment as early as possible because the interest charged will be less for each day early that you pay - making a lower final payment amount. On your mortgage loan, however, it makes sense to pay as close to the end of the "grace period" as possible (making sure, of course, that the payment is never "late" - after the grace period).

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DiscoBunny1979
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Re: Does a home mortgage use Simple or Compund Interest?

Post by DiscoBunny1979 » Mon Aug 05, 2013 10:32 am

dm200 wrote:On your mortgage loan, however, it makes sense to pay as close to the end of the "grace period" as possible (making sure, of course, that the payment is never "late" - after the grace period).
------------------

This is an example why some advice received on a message board might not be in your best interest. A Grace Period is a convenience at the bank's discretion. Paying continually during a Grace Period will set off red flags with the bank because technically you're 'late'. The due date is the due date. For instance, if the bill is due on the 1st of each month with a Grace Period until the 16th, you are still obligated to pay when it is due - the 1st of the month. Playing with the Grace Period is not wise in my opinion.

In answer to the OP, while most loans are calculated using a simple interest approach calculated on monthly interest, that might not be true when asking for a payoff of the loan. My bank for instance will charge for every day that the loan was outstanding and calculate a new payoff amount even though simple interest on a monthly basis was used to calculate monthly mortgage payments. Probably still simple interest, but it changes from a monthly calculation to a daily or set time frame calculation when asking for a payoff.

Retread
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Re: Does a home mortgage use Simple or Compund Interest?

Post by Retread » Mon Aug 05, 2013 10:46 am

DiscoBunny1979 wrote:
dm200 wrote:On your mortgage loan, however, it makes sense to pay as close to the end of the "grace period" as possible (making sure, of course, that the payment is never "late" - after the grace period).
------------------

This is an example why some advice received on a message board might not be in your best interest. A Grace Period is a convenience at the bank's discretion. Paying continually during a Grace Period will set off red flags with the bank because technically you're 'late'. The due date is the due date. For instance, if the bill is due on the 1st of each month with a Grace Period until the 16th, you are still obligated to pay when it is due - the 1st of the month. Playing with the Grace Period is not wise in my opinion.

In answer to the OP, while most loans are calculated using a simple interest approach calculated on monthly interest, that might not be true when asking for a payoff of the loan. My bank for instance will charge for every day that the loan was outstanding and calculate a new payoff amount even though simple interest on a monthly basis was used to calculate monthly mortgage payments. Probably still simple interest, but it changes from a monthly calculation to a daily or set time frame calculation when asking for a payoff.
You're dead wrong on this. Paying during the grace period constitutes timely payment in the eyes of the bank and according to the terms of the note. No red flags are set off at the bank by using the grace period.
Bruce
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scrabbler1
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Re: Does a home mortgage use Simple or Compund Interest?

Post by scrabbler1 » Mon Aug 05, 2013 10:51 am

The only minor variation I have ever seen in a home mortgage is between those which calculated interest accrued the same way each month regardless of the number of days in the month versus one which calculated the interest owed based on the number of days in that month. For example, a 31-day month accrued slightly more interest than a 30-day month (or February). The monthly payment did not vary, only how it was allocated between interest and principal.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Twins Fan » Mon Aug 05, 2013 10:57 am

Since no one wants to simply answer a simple question... :D
SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
The typical fixed rate mortgage is a simple interest loan. The amount of interest owed each month is figured off the outstanding balance that month.

(interest rate) 0.0xxx/12 (or x.xxx/1200) multiplied by outstanding blance = interest owed that month.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Mon Aug 05, 2013 12:34 pm

Definitely compound interest.

This is obvious from the way the calculation is made.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Kosmo » Mon Aug 05, 2013 1:28 pm

Twins Fan wrote:Since no one wants to simply answer a simple question... :D
SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
The typical fixed rate mortgage is a simple interest loan. The amount of interest owed each month is figured off the outstanding balance that month.

(interest rate) 0.0xxx/12 (or x.xxx/1200) multiplied by outstanding blance = interest owed that month.
Exactly. To use a physical example:

6% interest rate (per year), $100,000 balance. Interest due for the month = (.06/12)*100,000 = $500

Assume you make a payment of $1000 (principal payment is $500), then the next month the interest calculation is: (0.06/12)*99,500 = $497.50. The principal payment is then $502.50 (for a total payment of $1000).

If you were to sell or refinance or otherwise need to pay a fractional month's interest, the equation would be adjusted: (.06/365)*number of days since month start*balance = interest due

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dm200
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Re: Does a home mortgage use Simple or Compund Interest?

Post by dm200 » Mon Aug 05, 2013 4:33 pm

Retread wrote:
DiscoBunny1979 wrote:
dm200 wrote:On your mortgage loan, however, it makes sense to pay as close to the end of the "grace period" as possible (making sure, of course, that the payment is never "late" - after the grace period).
------------------

This is an example why some advice received on a message board might not be in your best interest. A Grace Period is a convenience at the bank's discretion. Paying continually during a Grace Period will set off red flags with the bank because technically you're 'late'. The due date is the due date. For instance, if the bill is due on the 1st of each month with a Grace Period until the 16th, you are still obligated to pay when it is due - the 1st of the month. Playing with the Grace Period is not wise in my opinion.

In answer to the OP, while most loans are calculated using a simple interest approach calculated on monthly interest, that might not be true when asking for a payoff of the loan. My bank for instance will charge for every day that the loan was outstanding and calculate a new payoff amount even though simple interest on a monthly basis was used to calculate monthly mortgage payments. Probably still simple interest, but it changes from a monthly calculation to a daily or set time frame calculation when asking for a payoff.
You're dead wrong on this. Paying during the grace period constitutes timely payment in the eyes of the bank and according to the terms of the note. No red flags are set off at the bank by using the grace period.
Bruce
The term "Grace Period" may have several different meanings, or be (rightly or wrongly) interpreted is several different ways.

First, a "wrong" meaning or interpretation - If an installment consumer loan (Let's say from a credit union) calls for monthly payments on the 18th of the month for, say, 60 months and the loan agreements/documents specify a "Late Fee" of 5% of the payment if the payment is received more than ten days past due, then you should plan to make the payments on or before the 18th. Paying on the 19th is late (although probably not a big deal) and if you paid on the 19th of each month every month, at the end of 60 months, you would still have a modest amount extra to pay - because you have paid a day late each month. The 12 days before the late fee is NOT a "grace period", in this case. I am in this business and know how this works first hand. So, the number of days before the imposition of a "Late Fee" is NOT a "Grace Period"!

Almost all US mortgages work differently and actually have a "Grace Period". I am NOT in the mortgage end of things, but am familiar with many aspects. If the mortgage documents say the payment is due on the 1stof the month and there is a "Grace Period" of, say ten days, (or some similar words) - then you are almost certainly safe to pay on the 9th of each month. Most mortgages loans charge the same amount of interest each month whether the payment is made early, just at the nominal 'due' date or within the grace period. Our own mortgage, for example, specifies due on the first with a grace period until the tenth. I know, in this case, that paying on the 8th or 9th of the month is just fine because we set up an automatic transfer from our checking account (a different institution) on the 8th or 9th. The setup of this automatic transfer with the dates were in the mortgage holders setup as choices.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Steelersfan » Mon Aug 05, 2013 7:19 pm

dm200 wrote:
Retread wrote:
DiscoBunny1979 wrote:
dm200 wrote:On your mortgage loan, however, it makes sense to pay as close to the end of the "grace period" as possible (making sure, of course, that the payment is never "late" - after the grace period).
------------------

This is an example why some advice received on a message board might not be in your best interest. A Grace Period is a convenience at the bank's discretion. Paying continually during a Grace Period will set off red flags with the bank because technically you're 'late'. The due date is the due date. For instance, if the bill is due on the 1st of each month with a Grace Period until the 16th, you are still obligated to pay when it is due - the 1st of the month. Playing with the Grace Period is not wise in my opinion.

In answer to the OP, while most loans are calculated using a simple interest approach calculated on monthly interest, that might not be true when asking for a payoff of the loan. My bank for instance will charge for every day that the loan was outstanding and calculate a new payoff amount even though simple interest on a monthly basis was used to calculate monthly mortgage payments. Probably still simple interest, but it changes from a monthly calculation to a daily or set time frame calculation when asking for a payoff.
You're dead wrong on this. Paying during the grace period constitutes timely payment in the eyes of the bank and according to the terms of the note. No red flags are set off at the bank by using the grace period.
Bruce
The term "Grace Period" may have several different meanings, or be (rightly or wrongly) interpreted is several different ways.

First, a "wrong" meaning or interpretation - If an installment consumer loan (Let's say from a credit union) calls for monthly payments on the 18th of the month for, say, 60 months and the loan agreements/documents specify a "Late Fee" of 5% of the payment if the payment is received more than ten days past due, then you should plan to make the payments on or before the 18th. Paying on the 19th is late (although probably not a big deal) and if you paid on the 19th of each month every month, at the end of 60 months, you would still have a modest amount extra to pay - because you have paid a day late each month. The 12 days before the late fee is NOT a "grace period", in this case. I am in this business and know how this works first hand. So, the number of days before the imposition of a "Late Fee" is NOT a "Grace Period"!

Almost all US mortgages work differently and actually have a "Grace Period". I am NOT in the mortgage end of things, but am familiar with many aspects. If the mortgage documents say the payment is due on the 1stof the month and there is a "Grace Period" of, say ten days, (or some similar words) - then you are almost certainly safe to pay on the 9th of each month. Most mortgages loans charge the same amount of interest each month whether the payment is made early, just at the nominal 'due' date or within the grace period. Our own mortgage, for example, specifies due on the first with a grace period until the tenth. I know, in this case, that paying on the 8th or 9th of the month is just fine because we set up an automatic transfer from our checking account (a different institution) on the 8th or 9th. The setup of this automatic transfer with the dates were in the mortgage holders setup as choices.
+1,

and I've got the credit reports and credit rating to back up that mortgage payments made during the "grace period" do not negatively affect either the outstanding balance you owe or your credit.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Mon Aug 05, 2013 10:24 pm

SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
Definitely compound interest (typically compounding monthly).

This is obvious from the way the calculation is made.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by BrandonBogle » Mon Aug 05, 2013 11:35 pm

555 wrote:
SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
Definitely compound interest (typically compounding monthly).

This is obvious from the way the calculation is made.
Incorrect. Unless you have a negative amortization loan, it is always simple interest.

http://en.m.wikipedia.org/wiki/Compound_interest
Compound interest arises when interest is added to the principal of a deposit or loan, so that, from that moment on, the interest that has been added also earns interest. This addition of interest to the principal is called compounding
While the interest and a payment is due monthly, outside of negative amortization loans, the principal does NOT gets outstanding interest added to it. When payoff time comes, the payoff is calculated with a daily accrued interest, but it still is not compounded.

Also, if you are 30 says late, you can do the math of Principal portion of payment + (Outstanding principal of loan * APR/12 * 2) to see how much interest you are paying. It would NOT compound to be Principal portion of payment + ((Outstanding principal of loan + (Outstanding principal of loan * APR/12)) * APR/12). That first one is simple interest at 30 days late and the second one is monthly compounding at 30 days late.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 12:21 am

Some people need to read this.
http://en.wikipedia.org/wiki/Compound_interest
Even a mere rudimentary understanding of how a mortgage works makes it clear that it uses compound interest.

Kosmo even gave an explicit example making it clear that you pay interest on interest (on interest on interest on interest etc.).

Just think about how an amortization calculation is made. It is calculated using compound interest. I don't know how anything could be more obvious (assuming a certain level of numeracy).

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Re: Does a home mortgage use Simple or Compund Interest?

Post by rkhusky » Tue Aug 06, 2013 7:29 am

555 wrote:Some people need to read this.
http://en.wikipedia.org/wiki/Compound_interest
Even a mere rudimentary understanding of how a mortgage works makes it clear that it uses compound interest.

Kosmo even gave an explicit example making it clear that you pay interest on interest (on interest on interest on interest etc.).

Just think about how an amortization calculation is made. It is calculated using compound interest. I don't know how anything could be more obvious (assuming a certain level of numeracy).
Compounding only occurs when interest is added to the principal. And then in the next month, one receives interest on the previous month's interest. If you have a savings account where the interest is sent to a non-interest bearing checking account (e.g. to pay for living expenses), you are not getting compound interest.

If you make regular monthly payments on a standard mortgage, you are paying the monthly interest charge and anything beyond that reduces the principal amount. An interest-only mortgage means that your principal does not change and you are only paying the interest charge, which does not change month to month, since your principal is remaining the same. There is no compounding of interest.

Home equity loans use daily interest calculations, like consumer loans mentioned above, but even here the interest calculation is based on the principal and there is no compounding of interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Userdc » Tue Aug 06, 2013 7:42 am

This may be a terminology difference between academia and the real world, but in the consumer loan space "simple interest" has a very specific meaning, and virtually all mortgage loans are NOT Simple Interest.

Auto loans are typically simple interest. Lets say you have a $300 monthly payment on your auto loan. A portion of that is directed to interest based on the actual number of days that have elapsed since your last payment. So if you pay earlier or later in the month, a different amount will be deducted from your payment to cover interest and the remainder will be directed to principal. With a simple interest loan you could typically pay smaller amounts throughout the month and reduce the amount of interest owed because you would be calculating the simple interest off a lower average balance.

Most conventional mortgage loans use a system call "interest in arrears". Each month, 30 days of interest are calculated based on the mortgage balance and interest rate. That full amount of interest is due at the end of the month (or typically the first of the following month). If you pay your payment a few days earlier or later, it does not affect the amount of interest due. Also, if you pay your mortgage in the grace period or become delinquent, the interest calculation for those future months uses a lower "scheduled balance" that assumes your balance had been reduced every month by on time payments. So you could skip 6 months of payments and pay them all at once and you would pay the same amount of interest (although you would likely pay significant late fees).

In both types of loans you will not pay "interest on interest" unless there is a modification to capitalize delinquent interest into the balance.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by BrandonBogle » Tue Aug 06, 2013 8:18 am

Userdc's description is accurate. That said, that still is NOT compounding interest (not saying Userdx was saying so, since the last paragraph says just as much).

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Re: Does a home mortgage use Simple or Compund Interest?

Post by BrandonBogle » Tue Aug 06, 2013 8:19 am

555 wrote:Some people need to read this.
http://en.wikipedia.org/wiki/Compound_interest
Even a mere rudimentary understanding of how a mortgage works makes it clear that it uses compound interest.

Kosmo even gave an explicit example making it clear that you pay interest on interest (on interest on interest on interest etc.).

Just think about how an amortization calculation is made. It is calculated using compound interest. I don't know how anything could be more obvious (assuming a certain level of numeracy).
In my post right above yours, I quoted the relevant passage in the same article. A mortgage without negative amortization is NOT compounding interest. A mortgage doesn't pass that essential sniff test that defines a compounding loan. I would reread the article and passage.

Kosmo's example is exactly what I refer to. In his/her example, the second month is NOT paying interest on the principal that was already paid down nor the interest from the first month. Hence, it is NOT compounding. He/she and I are posting the same concept.
Last edited by BrandonBogle on Tue Aug 06, 2013 8:22 am, edited 1 time in total.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by bsteiner » Tue Aug 06, 2013 8:21 am

Ignoring early or late payments, if, as is typical, the payments are monthly rather than annually, the interest is effectively compounded monthly. If you pay interest at, say, 4%, the cost is more if you pay monthly than if you pay annually. If you could pay annually, you would have use of the full year's interest until the end of the year.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by gwrvmd » Tue Aug 06, 2013 8:24 am

Mortgages are simple interest, however, if you miss a few payments you will find out how compound interest works..Gordon
Disciple of John Neff

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Re: Does a home mortgage use Simple or Compund Interest?

Post by BrandonBogle » Tue Aug 06, 2013 8:25 am

bsteiner wrote:Ignoring early or late payments, if, as is typical, the payments are monthly rather than annually, the interest is effectively compounded monthly. If you pay interest at, say, 4%, the cost is more if you pay monthly than if you pay annually. If you could pay annually, you would have use of the full year's interest until the end of the year.
I would suggest you punch in Kosmo's example above in a amortization calculator and look at what it has for interest paid at the end of the first year. Now take the original loan amount and multiply it by the loan APR. You will find this "annual interest" is HIGHER than what you would pay on the amortization calculator. That is because each monthly payment has reduced principal and each subsequent payment is calculated on a lesser amount.

Not a hard concept and all the numbers are completely verifyable with simple arithmetic.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Phineas J. Whoopee » Tue Aug 06, 2013 8:50 am

555 wrote:Some people need to read this.
http://en.wikipedia.org/wiki/Compound_interest
Even a mere rudimentary understanding of how a mortgage works makes it clear that it uses compound interest.

Kosmo even gave an explicit example making it clear that you pay interest on interest (on interest on interest on interest etc.).

Just think about how an amortization calculation is made. It is calculated using compound interest. I don't know how anything could be more obvious (assuming a certain level of numeracy).
I'll bite. Under the Exceptions heading of the Wikipedia article you suggested some of us read:
U.S. mortgages use an amortizing loan, not compound interest. With these loans, an amortization schedule is used to determine how to apply payments toward principal and interest. Interest generated on these loans is not added to the principal, but rather is paid off monthly as the payments are applied.
PJW

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 9:05 am

It's compound not simple.
Kosmo wrote:
Twins Fan wrote:Since no one wants to simply answer a simple question... :D
SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
The typical fixed rate mortgage is a simple interest loan. The amount of interest owed each month is figured off the outstanding balance that month.

(interest rate) 0.0xxx/12 (or x.xxx/1200) multiplied by outstanding blance = interest owed that month.
Exactly. To use a physical example:

6% interest rate (per year), $100,000 balance. Interest due for the month = (.06/12)*100,000 = $500

Assume you make a payment of $1000 (principal payment is $500), then the next month the interest calculation is: (0.06/12)*99,500 = $497.50. The principal payment is then $502.50 (for a total payment of $1000).
Okay let's see how Kosmo's example makes it completely obvious it's compound interest not simple. We start with an initial balance of 100000, and at each (monthly) time step we multiply by (1.005) (the monthly interest), then subtract 1000 (the monthly interest).

After 0 time periods (initial balance) the balance is
100000(1.005)^0

After 1 time period (after 1 payment) the balance is
(100000)(1.005)^1-(1000)^0

After 2 time periods (after 2 payment) the balance is
(100000)(1.005)^2-(1000)(1.005)^1-(1000)(1.005)^0

After 3 time periods the balance is
(100000)(1.005)^3-(1000)(1.005)^2-(1000)(1.005)^1-(1000)(1.005)^0

After 4 time periods the balance is
(100000)(1.005)^4-(1000)(1.005)^3-(1000)(1.005)^2-(1000)(1.005)^1-(1000)(1.005)^0

After 5 time periods the balance is
(100000)(1.005)^5-(1000)(1.005)^4-(1000)(1.005)^3-(1000)(1.005)^2-(1000)(1.005)^1-(1000)(1.005)^0

After n time periods the balance is
(100000)(1.005)^n-(1000)(1.005)^{n-1}-(1000)(1.005)^{n-2}-(1000)(1.005)^{n-3}...-(1000)(1.005)^3-(1000)(1.005)^2-(1000)(1.005)^1-(1000)(1.005)^0
which can also be written as
200000-(100000)(1.005)^n
(Just sum the geometric series.)

It's easy to see that interest is compounding every month on the initial principal and on every payment.

It's compound interest not simple.

That's how a standard mortgage works.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 9:29 am

This page
http://en.wikipedia.org/wiki/Annuity_%2 ... _theory%29
explains the basic math, using compound interest for mortgage calculations.

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BrandonBogle
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Re: Does a home mortgage use Simple or Compund Interest?

Post by BrandonBogle » Tue Aug 06, 2013 9:34 am

555, we will just have to agree to disagree.

IMO, until you are calculating a future payment inclusive of outstanding principal and previously paid interest, you are NOT compounding.

You feel otherwise and so be it. Thank you, but I am out of this conversation now.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 9:53 am

[OT comment removed by admin LadyGeek]

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Re: Does a home mortgage use Simple or Compund Interest?

Post by jimbojones » Tue Aug 06, 2013 10:25 am

The determination of whether the payment covers the accrued interest for the period is completely separate from the determination of simple vs compound interest. In a typical mortgage, amortization schedules have an implicit assumption that the interest is compounded monthly. Use the Excel function: PMT(rate,nper,PV). You'll calculate your exact mortgage payment using compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by dm200 » Tue Aug 06, 2013 10:35 am

Taking this discussion, perhaps, even further afield (or perhaps adding information), it is not just folks here that disagree about loan interest when regular, periodic payments are made. The "Annual Percentage Rate" (APR) is supposed to make comparisons easier and introduce a "standard" that should take such factors as compounding, prepaid finance charges, etc. into effect. In the U.S. a loan that has no prepaid finance charges and has regular periodic payments (each reducing the principal) is disclosed with an APR the same as the interest rate. So, for example, a loan with a 12.00% interest rate is disclosed with an APR of 12.00% as well.

In a previous employment life, I had some dealings with consumer lending calculations for lenders in the UK. That identical consumer loan that in the US has both the rate and APR as 12.00%, in the UK is disclosed with a rate of 12% (1% per month on the unpaid balance) and an APR of 12.68% (because of the monthly payments). It so happens that 12.00% compounded monthly is 12.68%.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Userdc » Tue Aug 06, 2013 10:43 am

I think there are some terminology differences here causing confusion. Some people are interpreting "compound interest" to mean "interest is paid on interest" and others use the word "compound" to indicate that payments of interest are due at periodic intervals prior to maturity.

Let's say that someone took out two non-amortizing loans, both with an interest rate of 5%:

Loan A has a balance of $10,000, due after one year.
Loan B has a balance of $10,500, due after two years.

In both loans, interest is paid annually.

So for Loan A, $10,500 is due after one year ($10K in principal, $500 in interest).
For Loan B, $525 in interest is due after one year and $11,025 is due after two years ($10,500 in principal, $525 in interest). Total interest paid is 10% of the loan amount.

Are either of these loans compound interest loans?

From the borrower perspective, Loan B is paying the same amount of interest as if the interest was paid at the end of the term. However, the lender of Loan B can use the benefit of recieving the interest after one year to go out and make more loans like loan A and earn interest on interest. So if the lender of Loan A is earning compound interest, in some respects, the borrower of Loan B is paying compound interest, even though they are paying exactly 2 x interest rate x loan balance.

Note that if you combine Loan A and Loan B into a single loan, you have an amortizing loan with a balance of $20,500, rate of 5%, and level annual payments of $11,025. All fixed rate amortizing loans are composed of smaller fixed rate non-amortizing loans with periodic payments of interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Spirit Rider » Tue Aug 06, 2013 2:07 pm

We really have a failure to communicate here. I think the problem here is one of definition. There really is a difference between interest that is calculated and assessed monthly and interest that compounds monthly, they are not the same.

Compound Interest is when the interest is applied to both the principal and accrued interest.

In a home mortgage the interest is only calculated and assessed monthly on the current principal. In a normal mortgage the payment exceeds the interest charge and all of the interest is paid and some of the principal is paid reducing the principal. There is NO interest to accrue and all subsequent interest charges are also on the principal only.

In a negative amortization mortgage, the payment is not sufficient to pay the interest charge thus the interest accrues and each subsequent interest calculation is compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 2:41 pm

jimbojones wrote:The determination of whether the payment covers the accrued interest for the period is completely separate from the determination of simple vs compound interest. In a typical mortgage, amortization schedules have an implicit assumption that the interest is compounded monthly. Use the Excel function: PMT(rate,nper,PV). You'll calculate your exact mortgage payment using compound interest.
Exactly. Since it is mathematically identical to compound interest, it is compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Spirit Rider » Tue Aug 06, 2013 2:47 pm

555 wrote:
jimbojones wrote:The determination of whether the payment covers the accrued interest for the period is completely separate from the determination of simple vs compound interest. In a typical mortgage, amortization schedules have an implicit assumption that the interest is compounded monthly. Use the Excel function: PMT(rate,nper,PV). You'll calculate your exact mortgage payment using compound interest.
Exactly. Since it is mathematically identical to compound interest, it is compound interest.
We are just going to have to disagree. If it does not constitute paying interest on accrued interest it is not compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by jimbojones » Tue Aug 06, 2013 3:04 pm

Spirit Rider wrote:We really have a failure to communicate here. I think the problem here is one of definition. There really is a difference between interest that is calculated and assessed monthly and interest that compounds monthly, they are not the same.

Compound Interest is when the interest is applied to both the principal and accrued interest.

In a home mortgage the interest is only calculated and assessed monthly on the current principal. In a normal mortgage the payment exceeds the interest charge and all of the interest is paid and some of the principal is paid reducing the principal. There is NO interest to accrue and all subsequent interest charges are also on the principal only.

In a negative amortization mortgage, the payment is not sufficient to pay the interest charge thus the interest accrues and each subsequent interest calculation is compound interest.
Say you had a $100 in a savings account that paid 12% APR, compounded monthly. After one month you have $101, after two you have $102.01, etc. up to $112.68 at the end of 12 months.

Now, instead of leaving everything in the account, you withdraw $1 at the instant of the interest payment. After one month there is $100 in the account ($100+$1-$1) and there will always be $100 in the account.

Does the second example magically transfer your account from compounding interest to simple interest?

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Re: Does a home mortgage use Simple or Compund Interest?

Post by rkhusky » Tue Aug 06, 2013 3:19 pm

jimbojones wrote:
Spirit Rider wrote:We really have a failure to communicate here. I think the problem here is one of definition. There really is a difference between interest that is calculated and assessed monthly and interest that compounds monthly, they are not the same.

Compound Interest is when the interest is applied to both the principal and accrued interest.

In a home mortgage the interest is only calculated and assessed monthly on the current principal. In a normal mortgage the payment exceeds the interest charge and all of the interest is paid and some of the principal is paid reducing the principal. There is NO interest to accrue and all subsequent interest charges are also on the principal only.

In a negative amortization mortgage, the payment is not sufficient to pay the interest charge thus the interest accrues and each subsequent interest calculation is compound interest.
Say you had a $100 in a savings account that paid 12% APR, compounded monthly. After one month you have $101, after two you have $102.01, etc. up to $112.68 at the end of 12 months.

Now, instead of leaving everything in the account, you withdraw $1 at the instant of the interest payment. After one month there is $100 in the account ($100+$1-$1) and there will always be $100 in the account.

Does the second example magically transfer your account from compounding interest to simple interest?
Yes, because in the second example you are no longer receiving interest on the re-invested interest. Hence you are not receiving the compounding of your interest.

With simple interest, the value of your investment grows linearly with time (example 1). With compound interest, the value of your investment grows exponentially with time (example 2).

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Petunia » Tue Aug 06, 2013 4:28 pm

555 wrote:
Exactly. Since it is mathematically identical to compound interest, it is compound interest.
The formula for compound interest is A = P( 1 + r/n)^nt

The formula for simple interest is I = Prt

There two are not mathematically indentical.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Twins Fan » Tue Aug 06, 2013 5:35 pm

Well, hopefully the OP got their question answered??? :D

OP, as you can see, one person says compound and everyone else says something different. You make the call.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Cyclone » Tue Aug 06, 2013 6:16 pm

I don't know what you call it, but I know it isn't simple interest. I work in a bank, and one of my jobs is to make sure the new home mortgage loans are NOT set to simple interest. What this means is that I make sure the little box in front of the simple interest box is not checked in the loan's profile in our data system. I don't remember if "compound interest" is one of the other choices - I am on vacation this week and everyone will have to wait until next week when I can look. I have found a few home mortgage loans that were set to simple interest, and the interest calculations were not what they should be (but the difference was usually only a few dollars a month). The formula used is: principal balance times (interest rate / 12).

Home mortgage loans are not considered late unless your payment arrives AFTER the grace period date. Beware about paying at a bank branch - sometimes those don't count as accepted until the check actually arrives at the loan service department.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Petunia » Tue Aug 06, 2013 6:28 pm

Cyclone wrote:I don't know what you call it, but I know it isn't simple interest. I work in a bank, and one of my jobs is to make sure the new home mortgage loans are NOT set to simple interest. What this means is that I make sure the little box in front of the simple interest box is not checked in the loan's profile in our data system. I don't remember if "compound interest" is one of the other choices - I am on vacation this week and everyone will have to wait until next week when I can look. I have found a few home mortgage loans that were set to simple interest, and the interest calculations were not what they should be (but the difference was usually only a few dollars a month). The formula used is: principal balance times (interest rate / 12).

Home mortgage loans are not considered late unless your payment arrives AFTER the grace period date. Beware about paying at a bank branch - sometimes those don't count as accepted until the check actually arrives at the loan service department.
This is the formula for simple interest. Google "formula for simple interest", and you will find countless sites stating the same thing.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by jimbojones » Tue Aug 06, 2013 6:35 pm

rkhusky wrote:
jimbojones wrote:
Spirit Rider wrote:We really have a failure to communicate here. I think the problem here is one of definition. There really is a difference between interest that is calculated and assessed monthly and interest that compounds monthly, they are not the same.

Compound Interest is when the interest is applied to both the principal and accrued interest.

In a home mortgage the interest is only calculated and assessed monthly on the current principal. In a normal mortgage the payment exceeds the interest charge and all of the interest is paid and some of the principal is paid reducing the principal. There is NO interest to accrue and all subsequent interest charges are also on the principal only.

In a negative amortization mortgage, the payment is not sufficient to pay the interest charge thus the interest accrues and each subsequent interest calculation is compound interest.
Say you had a $100 in a savings account that paid 12% APR, compounded monthly. After one month you have $101, after two you have $102.01, etc. up to $112.68 at the end of 12 months.

Now, instead of leaving everything in the account, you withdraw $1 at the instant of the interest payment. After one month there is $100 in the account ($100+$1-$1) and there will always be $100 in the account.

Does the second example magically transfer your account from compounding interest to simple interest?
Yes, because in the second example you are no longer receiving interest on the re-invested interest. Hence you are not receiving the compounding of your interest.

With simple interest, the value of your investment grows linearly with time (example 1). With compound interest, the value of your investment grows exponentially with time (example 2).
The deposit/loan is EITHER simple interest or compound interest. It is contractually agreed upon at the beginning. It does not change based on how you withdraw/pay.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by dm200 » Tue Aug 06, 2013 7:50 pm

The deposit/loan is EITHER simple interest or compound interest. It is contractually agreed upon at the beginning. It does not change based on how you withdraw/pay.
On the deposit side, not all actions the depositor may take are set for the term of the deposit. it is very common, for example, that a bank CD or credit union certificate allows optional (with no penalty) withdrawal of periodic interest. So, if you have a credit union certificate that pays monthly dividends (interest) to the certificate - you could let it compound over the certificate life or withdraw each month and it does not "compound".

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Re: Does a home mortgage use Simple or Compund Interest?

Post by mille424 » Tue Aug 06, 2013 7:51 pm

Everyone arguing for simple interest please explain the following phenomenon.

I used the bankrate.com calculator to get these numbers
http://www.bankrate.com/calculators/mor ... lator.aspx

Consider a 30yr $100,000 loan with 5% annual interest. The total interest paid on the loan is $93,255.78

If you make an additional payment to principal of $500 in the first month the total interest paid on the loan becomes $91,545.69, a difference of $1,710.09.

If we assume the $500 additional principal payment accrued simple interest on the entire amount for the remaining 359 months would be equal to ($500)*(5%/12)*(359)= 747.92.

How would you account for the additional $900+ in interest savings mathematically?

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 8:11 pm

I think people need to realize that when you "add" (e.g.) 0.5% interest, you are actually multiplying by 1.005. Perhaps people's inability to grasp this concept is the reason they can't recognize that a mortgage uses compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Twins Fan » Tue Aug 06, 2013 8:42 pm

mille424 wrote:Everyone arguing for simple interest please explain the following phenomenon.

I used the bankrate.com calculator to get these numbers
http://www.bankrate.com/calculators/mor ... lator.aspx

Consider a 30yr $100,000 loan with 5% annual interest. The total interest paid on the loan is $93,255.78

If you make an additional payment to principal of $500 in the first month the total interest paid on the loan becomes $91,545.69, a difference of $1,710.09.

If we assume the $500 additional principal payment accrued simple interest on the entire amount for the remaining 359 months would be equal to ($500)*(5%/12)*(359)= 747.92.

How would you account for the additional $900+ in interest savings mathematically?
So, are you making the argument for compound principal payments?

There's nothing to assume about the $500 pre-payment. That knocked down the principal balance plain and simple. So, the next interest amount due is SIMPLY figured off the new principal balance, which is $500 ahead of schedule now.

You basically don't pay any interest on that $500 pre-payment. Hence, why it would be said one would get a guaranteed 5% return by paying a loan like the one above off early.

The pre-payment thing brings up a good point for the compounding argument. By pre-paying a mortgage, one accelerates paying down the principal which makes for less interest paid over the long run. So, if lowering the principal minimizes the interest, how does the word compounding fit anywhere in there with all that lowering and minimizing going on?
Last edited by Twins Fan on Tue Aug 06, 2013 8:47 pm, edited 1 time in total.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by Twins Fan » Tue Aug 06, 2013 8:44 pm

555 wrote:I think people need to realize that when you "add" (e.g.) 0.5% interest, you are actually multiplying by 1.005. Perhaps people's inability to grasp this concept is the reason they can't recognize that a mortgage uses compound interest.
What does adding 0.5% have to do with anything?

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Re: Does a home mortgage use Simple or Compund Interest?

Post by mille424 » Tue Aug 06, 2013 10:01 pm

Twins Fan wrote: So, are you making the argument for compound principal payments?
Not exactly.
Twins Fan wrote: There's nothing to assume about the $500 pre-payment. That knocked down the principal balance plain and simple. So, the next interest amount due is SIMPLY figured off the new principal balance, which is $500 ahead of schedule now.

You basically don't pay any interest on that $500 pre-payment. Hence, why it would be said one would get a guaranteed 5% return by paying a loan like the one above off early.
Show the math for this part. This is where the contention comes from. How much interest gets saved by paying the $500 ahead of schedule? How much should be saved if the interest rate is simple? How much should be saved if the interest rate is compound?

$500 with 359 remaining months at (5%/12) monthly interest from my previous post is $747.92.

$500 with 359 remaining months at (5%/12) interest compounded monthly is $1724.60 (using excel) is much closer to the actual interest saved from the bankrate calculator.

I would say my stance is that the mortgage is a series of simple interest payments that can more elegantly be described by a compound interest calculation. There is no "interest paid on interest" in the literal sense that's true, but calling a mortgage a simple interest loan I think misrepresents what's actually happening.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by LadyGeek » Tue Aug 06, 2013 10:14 pm

SavingCash - You got your answer in the first reply, and then a lot of deep-dive discussion ensued. It's what we do... :D

Was your question answered? If not, please post what you need help with.

To those using math calculations, please see this wiki article: Comparing Investments

Draw the cash flow diagram, setup the 6 financial variables, then figure out what needs to be plugged into Excel (or LibreOffice Calc). Getting the sign convention correct is important.
Wiki To some, the glass is half full. To others, the glass is half empty. To an engineer, it's twice the size it needs to be.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 10:46 pm

Twins Fan wrote:
555 wrote:I think people need to realize that when you "add" (e.g.) 0.5% interest, you are actually multiplying by 1.005. Perhaps people's inability to grasp this concept is the reason they can't recognize that a mortgage uses compound interest.
What does adding 0.5% have to do with anything?
It was what Kosmo chose as an example of monthly interest. It's just an example.

The general prinicipal is that "adding" interest is actually multiplying, and that's why mortgages use compound interest.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 11:03 pm

LadyGeek wrote:SavingCash - You got your answer in the first reply, and then a lot of deep-dive discussion ensued. It's what we do... :D

Was your question answered? If not, please post what you need help with.
No. The first reply was totally incorrect which is why it needed to be corrected.

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Re: Does a home mortgage use Simple or Compund Interest?

Post by JamesSFO » Tue Aug 06, 2013 11:07 pm

555 wrote: The general prinicipal [ed: principle?] is that "adding" interest is actually multiplying, and that's why mortgages use compound interest.

{{later post}}

No. The first reply was totally incorrect which is why it needed to be corrected.
Except that most US mortgages do NOT charge interest on interest, and thus are not considered to be compound interest loans. Check out the mortgage professor website (first response). The confusion is caused by the daily interest accrual approach on many (most?) loans which LOOKS a lot like compound interest.

The first reply was not incorrect nor are many of the websites that discuss this very issue...

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Re: Does a home mortgage use Simple or Compund Interest?

Post by 555 » Tue Aug 06, 2013 11:13 pm

Kosmo wrote:
Twins Fan wrote:Since no one wants to simply answer a simple question... :D
SavingCash wrote:Can someone explain how a home mortgage loan, fixed rate, works please? Is it simple interest or compund and if its compund would that be daily compound or something else? Thank you
The typical fixed rate mortgage is a simple interest loan. The amount of interest owed each month is figured off the outstanding balance that month.

(interest rate) 0.0xxx/12 (or x.xxx/1200) multiplied by outstanding blance = interest owed that month.
Exactly. To use a physical example:

6% interest rate (per year), $100,000 balance. Interest due for the month = (.06/12)*100,000 = $500

Assume you make a payment of $1000 (principal payment is $500), then the next month the interest calculation is: (0.06/12)*99,500 = $497.50. The principal payment is then $502.50 (for a total payment of $1000).

If you were to sell or refinance or otherwise need to pay a fractional month's interest, the equation would be adjusted: (.06/365)*number of days since month start*balance = interest due
Okay suppose you have a savings account that gives 0.5% interest per month. You start with $100,000 and withdraw $1000 each month. Clearly the savings account has compound interest (compounding monthly), and surely no-one would dispute this. Every month the balance in the savings account is identical to the balance on the mortgage. The math is identical. Both the savings account and the mortgage, use exactly the same math, and so obviously, the mortgage uses compound interest.

I just don't see why people aren't getting this basic math. It's just not that complicated.

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