Amortization Formula

Amortization Formula (Table of Contents)

• Amortization Formula
• Amortization Calculator
• Amortization Formula in Excel (With Excel Template)

Amortization Formula

Amortization is paying off debt amount periodically until the loan principal reduces to zero. The amount paid monthly is known as EMI, which is equated to monthly installments. EMI has a principal and interest components, which are calculated by the amortization formula. Amortization calculation depends on the principal, the rate of interest, and the 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 the below formula:-

And the formula for interest is as follows:-

Where,

• P = Principal
• 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 a home loan from a bank of $100,000 at the rate of interest of 10% for a period of 20 years. Now, we must 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 the interest formula.

• I = nƥt – P
• I = 12*965.0216*20 – 100,000
• I = $131,605.2

So, the 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 the lender as well as the borrower with systematic repayment.
• There are very fewer chances of error.
• The borrower can check the principal amount outstanding at any point in time.
• It creates transparency between the borrower and the lender.

Amortization is calculated for loan repayment. Amortization is used in personal, home, and Auto loan repayment schedule preparation. It gives deep details from starting till the maturity of the loan. If any borrower does part payment, his amortization schedule changes, and the effect of the same is visible on EMI or tenure. That means the borrower can request for tenure change where EMI tenure will reduce and his EMI amount will be the same, or he can request a change in EMI where his EMI amount will reduce and tenure will be the same. In loans, more prepayment is done will result in less interest as the 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

Amortization Formula in Excel (With Excel Template)

Now, let us see how amortization can be calculated by excel.

A couple took an auto loan from a bank of $10,000 at the rate of interest of 10% for a period of 2 years. Now, we have to calculate the EMI amount for the same.

Amortization in excel is calculated using the below formula:

= PMT(Rate,nper,pv)

In excel, one can use the below formula to calculate the amortization value:-

• For the calculation of interest paid during a specific period, we will use the 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 the number of payments below formula is used.

= NPER(Rate,pmt,pv)

• To calculate cumulative interest payment for periods n1 through n2.

=CUMIPMT(rate,nper,pv,n1,n2,0)

• To calculate the cumulative principal payment for periods n1 through n2.

=CUMIPRINC(rate,nper,pv,n1,n2,0)

• To calculate the principal paid in an EMI below formula is used.

=PPMT(rate,per,nper,pv)

Where,

• pv = Present value of the 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 an amortization schedule.

Below are steps to prepare an amortization schedule in excel.

• Put input of formula in a standard format.

Principal	$200,000
Rate of Interest	9%
Tenure(In years)	10

• Plot table for an amortization schedule. In the zero month column, put the balance as $200,000 and then put 1, 2, 3, and so on till the last month of EMI in the month field.

Month

EMI

Principal

Interest

Balance

• Calculate EMI with the below formula:-

= PMT(Rate,nper,pv)

• Calculate the principal with the below formula:-

=PPMT(rate,per,nper,pv)

• Now, interest will be:-

Interest = EMI – Principal

• The balance will be the previous balance minus the principal.

Balance = Previous Balance – Principal

• Repeat the same till last month, and we will get the amortization schedule.

Now, we will see an example of preparing an amortization schedule.

A person has taken an auto loan of $200,000 with a rate of interest of 9% for a tenure of 3 years and wants to prepare his amortization schedule.

Using the above formulas in excel, he gets an amortization schedule.

• Put input of formula in a standard format.

• Plot table for the amortization schedule. In the zero month column, put the balance as $200,000 and then put 1, 2, 3, and so on till the last month of EMI in the month field.

• Calculate EMI with the below formula:-

• Calculate the principal with the below formula:-

• Now, interest will be:-

• The balance will be the previous balance minus the principal.

• Repeat the same till last month, and he will get the below amortization schedule.

Month	EMI	Principal	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

An amortization schedule helps one to know when they have to pay EMI against their loan and the EMI, they need to pay, how much interest they have to pay on their loan, and what is the principal outstanding of the loan. It is a very systematic and easy way to track the repayment of the loan.

Amortization ends when the loan is matured, and the principal balance is zero. If the amount is not recovered from the borrower, then the interest accrued will be added to the outstanding amount, which leads to an increase in the principal of the loan, known as negative amortization.

Recommended Articles

This has been a guide to an Amortization formula. Here we discuss its uses along with practical examples. We also provide you with an Amortization Calculator with a downloadable excel template. You may also look at the following articles to learn more –

1. Formula for Quick Ratio
2. How To Calculate Marginal Cost?
3. Calculator for Debt Ratio Formula
4. Net Working Capital Formula