Question

Sanjay takes a personal loan of ₹6,00,000 at the rate of 12% per annum for 'n' years. The EMI using the flat rate method is ₹16,000. The value of 'n' is:

• A. 3
• B. 6
• C. 5
• D. 4

Answer 1

The Correct Option is C

Solution: The flat-rate EMI is computed using the following formula:

\[EMI = \frac{Loan Amount + Total Interest}{Number of Months}\]

Total interest is calculated under the flat rate method as:

\[Total Interest = Loan Amount \times Rate of Interest \times Time (in years)\]

Given a loan amount of 6,00,000 and a rate of interest of 12% (0.12), with the time period as \(n\) years:

\[Total Interest = 6,00,000 \times 0.12 \times n = 72,000 \times n\]

Substituting into the EMI formula:

\[16,000 = \frac{6,00,000 + 72,000n}{12n}\]

To eliminate the denominator, multiply both sides by 12n:

\[16,000 \times 12n = 6,00,000 + 72,000n\]

\[1,92,000n = 6,00,000 + 72,000n\]

Simplify the equation:

\[1,92,000n - 72,000n = 6,00,000\]

\[1,20,000n = 6,00,000\]

Solve for n:

\[n = \frac{6,00,000}{1,20,000} = 5\]

Final Answer: The value of n is: \(5\)