Amortization schedule
Encyclopedia
An amortization schedule is a table detailing each periodic payment on an amortizing loan
(typically a mortgage
), as generated by an amortization calculator
. Amortization
refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance. The percentage of interest versus principal in each payment is determined in an amortization schedule.
While a portion of every payment is applied towards both the interest
and the principal balance
of the loan, the exact amount applied to principal each time varies (with the remainder going to interest). An amortization schedule reveals the specific monetary amount put towards interest, as well as the specific amount put towards the principal balance, with each payment. Initially, a large portion of each payment is devoted to interest. As the loan matures, larger portions go towards paying down the principal.
Amortization schedules run in chronological order. The first payment is assumed to take place one full payment period after the loan was taken out, not on the first day (the amortization date) of the loan
. The last payment completely pays off the remainder of the loan
. Often, the last payment will be a slightly different amount than all earlier payments.
In addition to breaking down each payment into interest and principal portions, an amortization schedule also reveals interest
-paid-to-date, principal-paid-to-date, and the remaining principal balance on each payment date.
First, it should be known that rounding errors occur and depending how the lender accumulates these errors, the blended payment (principal + interest) may vary slightly some months to keep these errors from accumulating; or, the accumulated errors are adjusted for at the end of each year, or at the final loan payment.
There are a few crucial points worth noting when mortgaging a home with an amortized loan. First, there is substantial disparate allocation of the monthly payments toward the interest, especially during the first 18 years of the mortgage. In the example above, payment 1 allocates about 80-90% of the total payment towards interest and only $67.09 (or 10-20%) toward the Principal balance
. The exact percentage allocated towards payment of the principal depends on the interest rate. Not until payment 257 or 21 years into the loan does the payment allocation towards principal and interest even out and subsequently tip the majority of the monthly payment toward Principal balance pay down.
Second, understanding the above statement, the repetitive refinancing of an amortized mortgage loan, even with decreasing interest rates and decreasing Principal balance, can cause the borrower to pay over 500% of the value of the original loan amount. 'Re-amortization' or restarting the amortization schedule via a refinance causes the entire schedule to restart: the new loan will be 30 years from the refinance date, and initial payments on this loan will again be largely interest, not principal. If the rate is the same, say 8%, then the interest/principal allocation will be the same as at the start of the original loan (say, 90/10). This economically unfavorable situation is often mitigated by the apparent decrease in monthly payment and interest rate of a refinance, when in fact the borrower is increasing the total cost of the property. This fact is often (understandably) overlooked by borrowers.
Third, the payment on an amortized mortgage loan remains the same for the entire loan term, regardless of Principal balance owed. For example, the payment on the above scenario will remain $733.76 regardless if the Principal balance is $100,000 or $50,000. Paying down large chunks of the Principal balance in no way affects the monthly payment, it simply reduces the term of the loan and reduces the amount of interest that can be charged by the lender resulting in a quicker payoff.
To avoid these caveats of an amortizing mortgage loan many borrowers are choosing an interest-only loan
to satisfy their mortgage financing needs. Interest-only loans have their caveats as well which must be understood before choosing the mortgage payment term that is right for the individual borrower.
Example of O/S loan balance calculation:
Question: What is the loan balance at the end of year seven?
First, calculate the monthly payments by using the loan amount ($100,000) as present value, term as 240 (20 years x 12 months/year), Interest as .583333% (7%/12 months). This will give you a monthly payment of $775.30. The Present Value of an Annuity formula should be used here to solve for monthly payment.
Next, in order to find the outstanding loan balance you will need to find the present value of the remaining payments. Use the monthly payment of $775.30 as the payment function, the term will be 156 ((20-7)x12), and .583333% as the rate. This will give you an outstanding loan balance of $79,268.02. Again, the Present Value of an Annuity formula should be used.
This means that at the end of year seven the loan can be paid off in full for the amount of $79,268.02. Typically mortgage lenders will have a balloon payment clause in the contract that will charge a fee for early payment. This is because the lender will not get the same yield if loan balance is not held to maturity.
Similarly here is a table that shows both the interest and principle portions paid for the first two years.
Amortizing loan
In banking and finance, an amortizing loan is a loan where the principal of the loan is paid down over the life of the loan, according to some amortization schedule, typically through equal payments....
(typically a mortgage
Mortgage loan
A mortgage loan is a loan secured by real property through the use of a mortgage note which evidences the existence of the loan and the encumbrance of that realty through the granting of a mortgage which secures the loan...
), as generated by an amortization calculator
Amortization calculator
An amortization calculator is used to determine the periodic payment amount due on a loan , based on the amortization process....
. Amortization
Amortization
Amortization is the process of decreasing, or accounting for, an amount over a period. The word comes from Middle English amortisen to kill, alienate in mortmain, from Anglo-French amorteser, alteration of amortir, from Vulgar Latin admortire to kill, from Latin ad- + mort-, mors death.When used...
refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance. The percentage of interest versus principal in each payment is determined in an amortization schedule.
While a portion of every payment is applied towards both the interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
and the principal balance
Principal balance
Principal balance, in regards to a mortgage or other debt instrument, is the amount due and owing to satisfy the payoff of the underlying obligation....
of the loan, the exact amount applied to principal each time varies (with the remainder going to interest). An amortization schedule reveals the specific monetary amount put towards interest, as well as the specific amount put towards the principal balance, with each payment. Initially, a large portion of each payment is devoted to interest. As the loan matures, larger portions go towards paying down the principal.
Methods of amortization
There are different methods in which to arrive at an amortization schedule. These include:- Straight line (linear)
- Declining balance
- Annuity
- Bullet (all at once)
- Increasing balance (negative amortizationNegative amortizationIn finance, negative amortization, also known as NegAm, deferred interest or graduated payment mortgage, occurs whenever the loan payment for any period is less than the interest charged over that period so that the outstanding balance of the loan increases...
)
Amortization schedules run in chronological order. The first payment is assumed to take place one full payment period after the loan was taken out, not on the first day (the amortization date) of the loan
Loan
A loan is a type of debt. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the lender and the borrower....
. The last payment completely pays off the remainder of the loan
Loan
A loan is a type of debt. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the lender and the borrower....
. Often, the last payment will be a slightly different amount than all earlier payments.
In addition to breaking down each payment into interest and principal portions, an amortization schedule also reveals interest
Interest
Interest is a fee paid by a borrower of assets to the owner as a form of compensation for the use of the assets. It is most commonly the price paid for the use of borrowed money, or money earned by deposited funds....
-paid-to-date, principal-paid-to-date, and the remaining principal balance on each payment date.
Example amortization schedule
This amortization schedule is based on the following assumptions:First, it should be known that rounding errors occur and depending how the lender accumulates these errors, the blended payment (principal + interest) may vary slightly some months to keep these errors from accumulating; or, the accumulated errors are adjusted for at the end of each year, or at the final loan payment.
There are a few crucial points worth noting when mortgaging a home with an amortized loan. First, there is substantial disparate allocation of the monthly payments toward the interest, especially during the first 18 years of the mortgage. In the example above, payment 1 allocates about 80-90% of the total payment towards interest and only $67.09 (or 10-20%) toward the Principal balance
Principal balance
Principal balance, in regards to a mortgage or other debt instrument, is the amount due and owing to satisfy the payoff of the underlying obligation....
. The exact percentage allocated towards payment of the principal depends on the interest rate. Not until payment 257 or 21 years into the loan does the payment allocation towards principal and interest even out and subsequently tip the majority of the monthly payment toward Principal balance pay down.
Second, understanding the above statement, the repetitive refinancing of an amortized mortgage loan, even with decreasing interest rates and decreasing Principal balance, can cause the borrower to pay over 500% of the value of the original loan amount. 'Re-amortization' or restarting the amortization schedule via a refinance causes the entire schedule to restart: the new loan will be 30 years from the refinance date, and initial payments on this loan will again be largely interest, not principal. If the rate is the same, say 8%, then the interest/principal allocation will be the same as at the start of the original loan (say, 90/10). This economically unfavorable situation is often mitigated by the apparent decrease in monthly payment and interest rate of a refinance, when in fact the borrower is increasing the total cost of the property. This fact is often (understandably) overlooked by borrowers.
Third, the payment on an amortized mortgage loan remains the same for the entire loan term, regardless of Principal balance owed. For example, the payment on the above scenario will remain $733.76 regardless if the Principal balance is $100,000 or $50,000. Paying down large chunks of the Principal balance in no way affects the monthly payment, it simply reduces the term of the loan and reduces the amount of interest that can be charged by the lender resulting in a quicker payoff.
To avoid these caveats of an amortizing mortgage loan many borrowers are choosing an interest-only loan
Interest-only loan
An interest-only loan is a loan in which, for a set term, the borrower pays only the interest on the principal balance, with the principal balance unchanged...
to satisfy their mortgage financing needs. Interest-only loans have their caveats as well which must be understood before choosing the mortgage payment term that is right for the individual borrower.
Outstanding loan balance calculation
The outstanding loan balance at any given time during the term of a loan can be calculated by finding the present value of the remaining payments at the given interest rate. This amount will consist of principal only.Example of O/S loan balance calculation:
- Loan Amount= $100,000
- Term= 20 years
- Interest Rate = 7%
- Amortization is monthly
Question: What is the loan balance at the end of year seven?
First, calculate the monthly payments by using the loan amount ($100,000) as present value, term as 240 (20 years x 12 months/year), Interest as .583333% (7%/12 months). This will give you a monthly payment of $775.30. The Present Value of an Annuity formula should be used here to solve for monthly payment.
Next, in order to find the outstanding loan balance you will need to find the present value of the remaining payments. Use the monthly payment of $775.30 as the payment function, the term will be 156 ((20-7)x12), and .583333% as the rate. This will give you an outstanding loan balance of $79,268.02. Again, the Present Value of an Annuity formula should be used.
This means that at the end of year seven the loan can be paid off in full for the amount of $79,268.02. Typically mortgage lenders will have a balloon payment clause in the contract that will charge a fee for early payment. This is because the lender will not get the same yield if loan balance is not held to maturity.
Similarly here is a table that shows both the interest and principle portions paid for the first two years.
| Period | Interest | Principal | Balance |
|---|---|---|---|
| 1 | $583.33 | $191.97 | $99,808.03 |
| 2 | $582.21 | $193.09 | $99,614.95 |
| 3 | $581.09 | $194.21 | $99,420.74 |
| 4 | $579.95 | $195.34 | $99,225.39 |
| 5 | $578.81 | $196.48 | $99,028.91 |
| 6 | $577.67 | $197.63 | $98,831.28 |
| 7 | $576.52 | $198.78 | $98,632.50 |
| 8 | $575.36 | $199.94 | $98,432.55 |
| 9 | $574.19 | $201.11 | $98,231.44 |
| 10 | $573.02 | $202.28 | $98,029.16 |
| 11 | $571.84 | $203.46 | $97,825.70 |
| 12 | $570.65 | $204.65 | $97,621.05 |
| 13 | $569.46 | $205.84 | $97,415.21 |
| 14 | $568.26 | $207.04 | $97,208.16 |
| 15 | $567.05 | $208.25 | $96,999.91 |
| 16 | $565.83 | $209.47 | $96,790.45 |
| 17 | $564.61 | $210.69 | $96,579.76 |
| 18 | $563.38 | $211.92 | $96,367.84 |
| 19 | $562.15 | $213.15 | $96,154.69 |
| 20 | $560.90 | $214.40 | $95,940.29 |
| 21 | $559.65 | $215.65 | $95,724.64 |
| 22 | $558.39 | $216.91 | $95,507.74 |
| 23 | $557.13 | $218.17 | $95,289.57 |
| 24 | $555.86 | $219.44 | $95,070.13 |