## Tuesday, September 08, 2009

### EMI Calculation for Home loans

This is a popular topic where most of us need help nowadays. Though there are bank websites which will give Rs.X is the EMI for the loan amount of Rs.L @ R % per annum for a term of say N months. But it is very important for us to understand the underlying principle of this EMI.

EMI – Equated Monthly Installment

For the loan amount you have got, you need to pay back the principal as well as the interest. But altogether you can’t repay the same. So you are splitting your debt (Principal + interest) to the financial institution in an equal way so that you can set aside a fixed amount every month for repayment.

Assume the loan amount (L) is Rs.1,00,000/- @ rate (R%) 12 for term (N) of 12 months.

Before calculating EMI, you need to convert rate percent per annum as rate per month – i.e., divide R% by (12 x 100)

Divide by 100 to convert to absolute number from percentage and 12 to get monthly rate value.

So let us recalculate as r = R/(12*100)

In our case, r = 12/(12*100) = 0.01

EMI = (P * r) * {[(1+r)^N] / [((1+r)^N) – 1]}

Principal - 100000
Rate per annum - 12 = 0.01
Term (in months) - 12
EMI = 8885

Month NoOutstandingInt PaidPrincipal PaidEMIBalanceRate
1100000100078858885921150.01
29211592179648885841510.01
38415184280438885761080.01
47610876181248885679840.01
56798468082058885597790.01
65977959882878885514920.01
75149251583708885431220.01
84312243184548885346680.01
93466834785388885261300.01
102613026186248885175070.01
11175071758710888587970.01
128797888797888500.01

How to generate the table?

1. EMI and rate has been fixed now.
2. Now write numbers against the month column equal to the loan term that is already known to us.
3. For month 1, outstanding = loan amount (i.e. Principal)
4. Int Paid = outstanding * r [in this case r = 0.01]
5. Principal Paid = EMI – Int Paid
6. Balance = Outstanding – Principal Paid
7. Outstanding for next month is the balance of the previous month

Thus keep going for the rest of the months. You can also prepare an excel in the same format and copy formulae and generate the EMI and the table.

If you see, EMI = Principal + Interest and thus you are paying both interest and principal every month. If you observe, the interest you pay will keep decreasing with the progress of time and the principal keeps on increasing with the progress of time.