Q.XYZ company borrows ₹3,00,000 with 7% annual interest rate for 4 years. Calculate EMI under Reducing Balance method.

The key idea is that under the Reducing Balance method, interest is charged only on the outstanding principal, so the EMI is calculated using the standard annuity formula $EMI = P\times\dfrac{r(1+r)^n}{(1+r)^n-1}$.

Step 1: Identify the variables

• Principal $P = 3,00,000$
• Annual interest rate $= 7\%$, so monthly rate $r = \dfrac{7}{1200} = 0.0058333$
• Tenure $n = 4 \text{ years} = 48 \text{ months}$

Step 2: Compute step-by-step

• $(1+r)^n = (1.0058333)^{48} \approx 1.32205$
• Numerator: $r(1+r)^n = 0.0058333 \times 1.32205 \approx 0.0077120$
• Denominator: $(1+r)^n - 1 = 1.32205 - 1 = 0.32205$
• $EMI = 3,00,000 \times \dfrac{0.0077120}{0.32205} = 3,00,000 \times 0.0239462 \approx 7183.87$

Understanding the Reducing Balance Method

When you borrow money, the interest you pay each month depends on how much principal is still unpaid. Under the Reducing Balance method (also called the declining balance method), each EMI payment first covers the interest on the outstanding amount, and the remainder reduces the principal. This is the standard method used by banks for home loans, car loans, and personal loans in India.

The key formula for EMI under this method is:

Where:

• $P$ = principal loan amount (₹3,00,000)
• $r$ = monthly interest rate (annual rate ÷ 12)
• $n$ = total number of monthly instalments (years × 12)

This formula ensures that every EMI is the same amount throughout the loan tenure — that's why it's called an equated monthly instalment.

Step-by-Step Calculation

1. Convert annual interest rate to monthly rate

The annual interest rate is 7%. Since EMI is paid monthly, we need the monthly rate:

It's best to keep this as a fraction: $r = \frac{7}{1200}$.

2. Find the total number of payments

Loan tenure is 4 years, with monthly payments:

3. Calculate $(1+r)^n$

We need $\left(1 + \frac{7}{1200}\right)^{48}$. Building it up from squares:

$(1.00583333)^2 = 1.01170139$

$(1.00583333)^4 = 1.023539$

$(1.00583333)^8 = 1.047632$

$(1.00583333)^{16} = 1.097533$

$(1.00583333)^{32} = 1.204578$

$(1.00583333)^{48} = (1.00583333)^{32} \times (1.00583333)^{16} = 1.204578 \times 1.097533 = 1.322054$

So $(1+r)^n \approx 1.32205$.

4. Apply the EMI formula

The denominator is $1.32205 - 1 = 0.32205$, and the numerator is $0.00583333 \times 1.32205 = 0.0077120$, so

Rounding to the nearest rupee, the EMI is ₹7,184.

Verification (Optional but Insightful)

You can check this by constructing a small amortisation table for the first few months (interest = 7%/12 of the outstanding balance, principal repaid = EMI − interest):

Notice how the interest portion decreases each month because the outstanding principal is reducing. The EMI stays constant at ₹7,184 throughout.