Q.Rajesh borrows ₹6,00,000 with 9% annual interest rate for 5 years. Calculate EMI under Reducing Balance method.

The key idea is that under the Reducing Balance method, EMI is calculated using the formula for an equated monthly instalment, where interest is charged only on the outstanding principal.

Step 1: Convert annual rate to monthly rate and find number of instalments.

Monthly interest rate $r = \frac{9}{12 \times 100} = 0.0075$ (or 0.75% per month).

Number of months $n = 5 \times 12 = 60$.

Step 2: Apply the EMI formula.

The standard formula is:

where $P = 6,00,000$, $r = 0.0075$, $n = 60$.

Step 3: Compute the value.

First, $(1+r)^n = (1.0075)^{60}$. Using approximation or calculator: …

The Reducing Balance method (also called the Declining Balance method) is the standard way most banks calculate EMIs. Unlike the Flat Rate method (where interest is charged on the full principal for the entire tenure), the Reducing Balance method charges interest only on the outstanding principal after each payment. This means as you repay, the interest portion of your EMI decreases and the principal portion increases — but the EMI itself stays constant.

Why does this matter? Because it’s fairer to the borrower. You pay interest only on what you still owe, not on what you’ve already repaid. The formula that gives this constant monthly payment comes from the idea that the present value of all future EMIs must equal the loan amount today.

Let’s work through Rajesh’s numbers step by step.

1. Identify the inputs

   • Principal, $P = ₹6,00,000$
   • Annual interest rate = 9%
   • Tenure = 5 years
   • Since EMI is monthly, we need the monthly interest rate and the number of monthly instalments.
   • Monthly interest rate, $r = \frac{9\%}{12} = 0.75\% = 0.0075$ (in decimal)
   • Number of monthly instalments, $n = 5 \times 12 = 60$

2. Recall the EMI formula

   The standard formula for EMI under Reducing Balance is:

This formula comes from equating the loan amount to the sum of the present values of all future EMIs, discounted at the monthly rate $r$.

3. Compute $(1+r)^n$ We need $(1.0075)^{60}$. This is the only heavy calculation. You can do it stepwise or use a calculator. Let’s compute carefully:
   • $(1.0075)^2 = 1.01505625$
   • $(1.0075)^4 = (1.01505625)^2 \approx 1.030339$
   • $(1.0075)^8 = (1.030339)^2 \approx 1.061599$
   • $(1.0075)^{16} = (1.061599)^2 \approx 1.126993$
   • $(1.0075)^{32} = (1.126993)^2 \approx 1.270114$
   • Now $(1.0075)^{60} = (1.0075)^{32} \times (1.0075)^{16} \times (1.0075)^8 \times (1.0075)^4$ $= 1.270114 \times 1.126993 \times 1.061599 \times 1.030339$ Multiply stepwise: $1.270114 \times 1.126993 \approx 1.431379$ $1.431379 \times 1.061599 \approx 1.519467$ $1.519467 \times 1.030339 \approx 1.565681$ …