Skip to content
Exercise 7.3 · Q1

Q.Mohan takes a loan of ₹5,00,000 with 8% annual interest rate for 6 years. Calculate EMI under Flat-Rate system.

Arunachal CbseNCERTSubjective· 3mImportance★★★★★
42% · 30/72 Questions
✓ Free question

Under the flat-rate system, interest is charged on the full principal for the entire loan tenure, not on the reducing balance. The total interest is ₹2,40,000, making the total repayment ₹7,40,000 over 72 months. The EMI is therefore ₹10,277.78 (rounded to the nearest paisa).

The Concept: Why Flat-Rate EMI Works This Way

Most people intuitively think of loans like a home loan — you pay interest only on the remaining principal each month. That’s the reducing-balance method. But the flat-rate system is different, and it’s often used for personal loans, car loans, or consumer durables in India.

Here’s the key: in a flat-rate loan, the interest is calculated once on the entire loan amount for the full tenure, and then added to the principal. The total amount (principal + total interest) is then divided equally across all months. This means you pay the same EMI every month, but the interest component in each EMI is much higher than it would be under a reducing-balance system for the same rate.

Watch out

Common Pitfall

Students often mistakenly apply the reducing-balance EMI formula here. That formula uses P⋅r(1+r)n(1+r)n−1P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}, which is wrong for flat-rate. Flat-rate is simpler: just add the total interest to the principal and divide by the number of months.

Step-by-Step Calculation

Let’s break it down into clear steps.

1. Identify the given values.

  • Principal, P=₹5,00,000P = ₹5,00,000
  • Annual interest rate, R=8%R = 8\% per annum
  • Loan tenure, T=6T = 6 years

2. Calculate the total interest for the entire loan period.

Since interest is charged on the full principal for the full 6 years:

Total Interest=P×R100×T\text{Total Interest} = P \times \frac{R}{100} \times T

Substitute the values:

Total Interest=5,00,000×8100×6\text{Total Interest} = 5,00,000 \times \frac{8}{100} \times 6

First, compute 5,00,000×8100=5,00,000×0.08=40,0005,00,000 \times \frac{8}{100} = 5,00,000 \times 0.08 = 40,000.

Then, 40,000×6=2,40,00040,000 \times 6 = 2,40,000.

So, the total interest payable over 6 years is ₹2,40,000.

Tip

Shortcut

You can think of it as: 8% of ₹5,00,000 is ₹40,000 per year. For 6 years, that’s 6×40,000=₹2,40,0006 \times 40,000 = ₹2,40,000. No need to overcomplicate.

3. Find the total amount to be repaid.

This is simply the principal plus the total interest:

Total Repayment=P+Total Interest=5,00,000+2,40,000=₹7,40,000\text{Total Repayment} = P + \text{Total Interest} = 5,00,000 + 2,40,000 = ₹7,40,000

4. Determine the number of monthly instalments.

The loan is for 6 years, so:

n=6×12=72 monthsn = 6 \times 12 = 72 \text{ months}

5. Compute the EMI.

The EMI is the total repayment divided equally over the number of months:

EMI=Total Repaymentn=7,40,00072\text{EMI} = \frac{\text{Total Repayment}}{n} = \frac{7,40,000}{72}

Now perform the division:

7,40,00072=7,40,000÷472÷4=1,85,00018\frac{7,40,000}{72} = \frac{7,40,000 \div 4}{72 \div 4} = \frac{1,85,000}{18}

Simplify further: 1,85,000÷181,85,000 \div 18.

  • 18×10,277=1,84,98618 \times 10,277 = 1,84,986
  • Remainder: 1,85,000−1,84,986=141,85,000 - 1,84,986 = 14 So, 10,277+1418=10,277+0.777...=10,277.777...10,277 + \frac{14}{18} = 10,277 + 0.777... = 10,277.777...

Rounding to the nearest paisa (two decimal places), we get ₹10,277.78.

Flat-Rate EMI Formula:

EMI=P+(P×R100×T)T×12\text{EMI} = \frac{P + \left(P \times \frac{R}{100} \times T\right)}{T \times 12}

Where PP is principal, RR is annual rate in %, TT is tenure in years.

Final Answer

✓Final answer

The EMI under the flat-rate system is ₹10,277.78 per month.

Unlock everything free for 14 days

  • Full step-by-step solutions
  • Concept-first explanations
  • Methods, shortcuts & mistakes
  • PYQ mapping + timed mock tests

Full access for 14 days. No credit card required.