Loan EMIs and Interest Calculations

Some banks are offering loan at 10% some at 11% and some at 12%. Most people think that this is the percentage of interest calculated yearly. After taking loans they get shocked when they see that two borrowers borrowing at same rate of interest of are paying different Equated Monthly Installments (EMIs). Well that is because of one more factor in calculating EMIs that is called reducing frequency. We will talk about reducing frequency in this article and see how they affect the loan EMIs. In general this article will try to explain how EMIs are actually calculated.

When you take loan from a bank they tell you an interest rate which they would be charging on the loaned money. But there are two ways in which they calculate EMIs - one is flat rate system other is reducing balance system. For example you took a loan of 100000 for 20 years and interest rate charged is 10% per annum. Under flat rate system the EMI is calculated as follows:

Interest each year = 10000
total interest = 10000 x 20 = 200000
principle = 100000
total returned money = principle + total interest = 300000
EMI = total returned money / total months = 300000 / (20 x 12) = 1250

Reducing system can be further divided into many systems based on Reducing Frequency. What is this Reducing Frequency? When you repay your loan as EMIs, it has two parts - an interest part and a principle part. How frequently the principle returned, as part of EMI, is subtracted from the remaining balance is called the Reducing Frequency. Suppose the principle returned is subtracted every month from the remaining balance then then balance keeps on reducing each month and interest is calculated on the remaining amount. In this case the reducing frequency is monthly. If the principle returned is subtract once in a year then the reducing frequency is yearly. In that case you end up paying interest on the amount which you had already returned. The more the reducing frequency for a loan the better it is for you (the borrower). How lets see,

The EMI of this loan is calculated using following formula:

EMI = (principal x period interest) ((1 + period interest) ^n) /(m x ((1 + period interest)^n - 1))

where,
period interest = rate in % for the period divided 100
n = number of periods
m = months in a period

Now suppose the reducing frequency is monthly then
period = month
number of periods (n) in 20 years = 240 (i.e. 20x12)
period interest = (10/100)/12 (since 10% is annual interest rate for a month it will be divided by 12)
EMI = (100000 x 10/1200) ((1 + 10/1200)^240)/(1 x ((1 + 10/1200)^240 - 1))
i.e. EMI = 965

If reducing frequency is yearly then
period = a year
number of periods (n) in 20 years = 20
period interest = (10/100)
EMI = (100000 x 10/100) ((1 + 10/100)^20)/(12 x ((1 + 10/100)^20 - 1))
i.e. EMI = 978

These calculations applies to all kinds of loans whether it is House or Home Loan, Personal Loan, Education Loan or any other Loan.