Calculation of EMI or Amortization of Loans

People meet many large expenses — buying a car or house, starting a business, funding a trip — and often cannot pay for them outright, so they borrow money (take a loan) and repay it to the lender over a fixed length of time. A few basic terms frame every loan.

The principal is the original amount of money borrowed (or invested). Interest is the price a borrower pays for the use of the lender's money — the gap between what is borrowed and what is finally repaid. The rate of interest is that charge written as a percentage of the sum borrowed for a stated period, usually per year. The term of the loan is the length of time over which regular payments fully clear the debt.

Meaning of EMI. EMI stands for Equated Monthly Instalment — a fixed payment you make towards a loan on a set date each month. A loan is said to be amortized when it can be cleared by a sequence of equal payments made over equal periods. Each instalment splits into two parts:

• interest on the loan still outstanding, and
• repayment of a portion of the principal.

So with every payment part goes to interest and the rest chips away at the principal.

Methods of calculating EMI. The instalment can be worked out in two ways: the Flat Rate Method and the Reducing-Balance Method (Amortization).

Flat Rate Method. Here every interest charge is figured on the original loan amount, even though the balance is actually being paid down over time. You add the total principal to the total interest on that principal and divide by the number of monthly payments. With $P$ the principal, $I$ the total interest, and $n$ the number of months:

Reducing-Balance Method (Amortization). When a loan is amortized, at the start of any period the principal still outstanding equals the present value of the payments that remain. Using this idea, an interest-bearing loan of ₹$P$ at rate $i$ per period, cleared by $n$ equal payments of ₹$R$ each (a payment at the end of every period), obeys the amortization formulas. …