Q15

1 markMCQSection A

Using flat rate method, the EMI to repay a loan of Rs 20,000 in $2\frac{1}{2}$ years at an interest rate of 8% per annum is :

Q: Using flat rate method, the EMI to repay a loan of Rs 20,000 in $2\frac{1}{2}$ years at an interest rate of 8% per annum is :

The correct option is **(B) Rs 800**. **Calculation** - Simple interest = $P \times r \times t = 20000 \times 0.08 \times 2.5$ = Rs 4,000. - Total amount = $20000 + 4000$ = Rs 24,000. - Number of months = $2.5 \times 12 = 30$. - EMI = $24000 \div 30$ = **Rs 800**.

Financial Mathematics

EMI by Flat Rate Method

Options

(A)Rs 700

(B)Rs 800

(C)Rs 900

(D)Rs 100

Official Answer

The correct option is (B) Rs 800.

Calculation

Simple interest = $P \times r \times t = 20000 \times 0.08 \times 2.5$ = Rs 4,000.
Total amount = $20000 + 4000$ = Rs 24,000.
Number of months = $2.5 \times 12 = 30$ .
EMI = $24000 \div 30$ = Rs 800.

flat rate methodEMIsimple interestloan repaymentprincipal plus interest30 monthsRs 800financial mathematics

Marking Scheme

11 mark: correct option (B) Rs 800.
2Working (not required for MCQ but expected in a subjective version): interest 4,000; total 24,000; 30 months; EMI 800.

Hint

Flat rate: total interest = $P \times r \times t$ on the whole principal; EMI = (P + interest) / total months.

Quick Oral Answer

Under the flat rate method the interest of four thousand rupees is added to the twenty-thousand principal, and the twenty-four thousand total is divided by thirty months, giving an EMI of eight hundred rupees.

Analysis & Explanation

In the flat rate method, interest is charged on the full original principal for the entire tenure, then principal plus interest is split into equal monthly instalments.

Concept

Flat-rate interest = $P \times r \times t$ (simple interest on the original principal).
EMI = (Principal + Total interest) / (number of months).

Working

Interest = $20000 \times 8/100 \times 2.5$ = Rs 4,000.
Total repayable = 24,000 over 30 months.
EMI = $24000/30$ = Rs 800.

Why the key is right

(B) Rs 800 follows exactly from the flat-rate steps.

Why the distractors are wrong

(A) Rs 700 = $21000/30$ , understating the interest.
(C) Rs 900 = $27000/30$ , overstating the interest.
(D) Rs 100 ignores the principal entirely.

Common Mistakes

1Computing interest for only 1 year instead of 2.5 years, giving Rs 700.
2Using 24 or 25 months instead of 30 months for 2.5 years.
3Confusing the flat rate method with the reducing-balance EMI formula.

Interesting Facts

The flat rate method makes a loan look cheaper than it is; the effective (reducing-balance) rate is often nearly double the quoted flat rate.

Because flat-rate interest is charged on the full principal throughout, even after part of the loan is repaid, regulators encourage disclosure of the annual percentage rate for fair comparison.

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Frequently Asked Questions

How does flat rate EMI differ from reducing balance EMI?

Flat rate charges simple interest on the full original principal for the whole tenure, so EMI = ( $P + P \times r \times t$ )/months. Reducing balance charges interest only on the outstanding balance, giving lower total interest and a different EMI formula.

Why use 30 months for 2.5 years?

Because 2.5 years = $2.5 \times 12 = 30$ months, and EMI is a monthly instalment, so the total repayable amount is divided by 30.