Amortization Formula (Table of Contents)
Amortization Formula
Amortization refers to paying off debt amount on periodically over time till loan principle reduces to zero. Amount paid monthly is known as EMI which is equated monthly installment. EMI has both principal and interest component in it which is calculated by amortization formula. Amortization calculation depends on the principle, the rate of interest and time period of the loan. Amortization can be done manually or by excel formula for both are different.
Now, let us see how to calculate Amortization manually.
Monthly payment i.e. can be calculated by below formula:
And the formula for interest is as follows:
Where,
 P = Principle
 r= Rate of interest
 t = Time in terms of year
 n = Monthly payment in a year
 I = Interest
 ƥ = Monthly Payment or EMI amount
Example of Amortization Formula
Now, let’s see an example to understand the calculation.
A salaried person took home loan from a bank of $100,000 at the rate of interest of 10% for a period of 20 years. Now, we have to calculate the EMI amount and interest component paid to the bank.
 P = $100,000
 r= 10% i.e 0.1
 t = 20
 n = 12
Amortization is Calculated Using Below formula:
 ƥ = rP / n * [1(1+r/n)^{nt}]
 ƥ = 0.1 * 100,000 / 12 * [1(1+0.1/12)^{12*20}]
 ƥ = 965.0216
And now, to calculate interest paid we will put value in interest formula.
 I = nƥt – P
 I = 12*965.0216*20 – 100,000
 I = $131,605.2
So, interest paid on loan is $131,605.2.
Significance and Use of Amortization Formula
There are many uses of amortization they are as follows:
 It helps lender as well as the borrower for systematic repayment.
 There are very fewer chances of error.
 The borrower can check its principal amount outstanding at any point in time.
 It creates transparency between borrower and lender.
Amortization is calculated for loan repayment. Amortization is used in Personal loan, Home loan, Auto loan repayment schedule preparation. It gives deep details from starting till maturity of the loan. If any borrower does part payment his amortization schedule changes and effect of same is visible on EMI or tenure that means borrower can request for tenure change where EMI tenure will reduce and his EMI amount will be same or he can request for the change in EMI where EMI amount will reduce and tenure will be the same. In loans, more prepayment is done will result in less interest as principal balance will reduce. By using amortization calculation became very easy even in the above scenario.
Amortization Calculator
You can use the following Amortization Formula Calculator
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Amortization Formula =  
Amortization Formula = 
 

Amortization Formula in Excel (With Excel Template)
Now, let us see how amortization can be calculated by excel.
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A couple took an auto loan from a bank of $10,000 at the rate of interest of 10% for the period of 2 years. Now, we have to calculate EMI amount for the same.
Amortization in excel is Calculated Using Below formula:
= PMT(Rate,nper,pv)
In excel one can use below formula to calculate amortization value:
 For calculation of interest paid during a specific period, we will use below formula.
=ISPMT(Rate,per,nper,pv)
 To calculate the amount of payment in a period below formula is used.
= PMT(Rate,nper,pv)
 To calculate a number of payment below formula is used.
= NPER(Rate,pmt,pv)
 To calculate cumulative interest payment for period n1 through n2.
=CUMIPMT(rate,nper,pv,n1,n2,0)
 To calculate cumulative principle payment for period n1 through n2.
=CUMIPRINC(rate,nper,pv,n1,n2,0)
 To calculate principle paid in an EMI below formula is used.
=PPMT(rate,per,nper,pv)
Where,
 pv = Present value of loan
 pmt = Payment per period
 nper = Number of payment period
 rate = Rate of interest
Through the above formula repayment schedule for a loan over a period is prepared which is known as amortization schedule.
Below are steps to prepare amortization schedule in excel.
 Put input of formula in a standard format.
Principle  $200,000 
Rate of Interest  9% 
Tenure(In years)  10 
 Plot table for an amortization schedule. In zero month column put balance as $200,000 and then put 1, 2, 3 and so on till last month of EMI in the month field.
Month  EMI  Principle  Interest  Balance 
 Calculate EMI with below formula:
= PMT(Rate,nper,pv)
 Calculate principle with below formula:
=PPMT(rate,per,nper,pv)
 Now, interest will be:
Interest = EMI – Principle
 Balance will be previous balance minus principle.
Balance = Previous Balance – Principle
 Repeat the same till last month and we will get amortization schedule.
Now, we will see an example to prepare amortization schedule.
A person has taken the auto loan of $200,000 with the rate of interest 9% for the tenure of 3 years and he wants to prepare his amortization schedule.
Using the above formulas in excel he gets amortization schedule.
 Put input of formula in a standard format.
 Plot table for the amortization schedule. In zero month column put balance as $200,000 and then put 1, 2, 3 and so on till last month of EMI in the month field.
 Calculate EMI with below formula:
 Calculate principle with below formula:
 Now, interest will be:
 The balance will be previous balance minus principle.
 Repeat the same till last month and he will get below amortization schedule.
Month  EMI  Principle  Interest  Balance 
0  200,000  
1  6,360  4,860  1,500  195,140 
2  6,360  4,896  1,464  190,244 
3  6,360  4,933  1,427  185,311 
4  6,360  4,970  1,390  180,340 
5  6,360  5,007  1,353  175,333 
6  6,360  5,045  1,315  170,288 
7  6,360  5,083  1,277  165,205 
8  6,360  5,121  1,239  160,084 
9  6,360  5,159  1,201  154,925 
10  6,360  5,198  1,162  149,727 
11  6,360  5,237  1,123  144,490 
12  6,360  5,276  1,084  139,214 
13  6,360  5,316  1,044  133,898 
14  6,360  5,356  1,004  128,542 
15  6,360  5,396  964  123,146 
16  6,360  5,436  924  117,710 
17  6,360  5,477  883  112,233 
18  6,360  5,518  842  106,715 
19  6,360  5,560  800  101,155 
20  6,360  5,601  759  95,554 
21  6,360  5,643  717  89,911 
22  6,360  5,686  674  84,225 
23  6,360  5,728  632  78,497 
24  6,360  5,771  589  72,725 
25  6,360  5,815  545  66,911 
26  6,360  5,858  502  61,053 
27  6,360  5,902  458  55,151 
28  6,360  5,946  414  49,204 
29  6,360  5,991  369  43,214 
30  6,360  6,036  324  37,178 
31  6,360  6,081  279  31,097 
32  6,360  6,127  233  24,970 
33  6,360  6,173  187  18,797 
34  6,360  6,219  141  12,578 
35  6,360  6,266  94  6,313 
36  6,360  6,313  47  0 
Amortization Schedule
Amortization schedule helps one to know when he has to pay EMI against his loan and what is the EMI which he needs to pay, how much interest he has to pay on his loan, what is the principal outstanding of the loan. It is a very systematic and easy way to track repayment of the loan.
Amortization ends when the loan is matured and the principle balance is zero. If the amount is not recovered from borrower then interest accrued will be added to the outstanding amount which leads to an increase in the principle of the loan and this is known as negative amortization.
Recommended Articles
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