To calculate the value of each installment, we use the formula for equated annual installments under compound interest:

$EMI = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1}$

Where:

• $P$ = Principal amount (loan amount) = Rs. 3,31,000
• $r$ = Annual interest rate = 10% = 0.10
• $n$ = Number of installments (years) = 3

Step 1: Calculate the effective interest factor

$(1 + r)^n = (1 + 0.10)^3 = 1.1^3 = 1.331$

Step 2: Plug into the EMI formula

$EMI = \frac{331000 \cdot 0.10 \cdot 1.331}{1.331 - 1}$

Simplify the numerator and denominator:

• Numerator: $331000 \cdot 0.10 \cdot 1.331 = 44096.1$
• Denominator: $1.331 - 1 = 0.331$

$EMI = \frac{44096.1}{0.331} \approx 133,200.3$

Final Answer:

The closest value is 133,300 (Option 1).

Would you like a breakdown of the steps or a detailed derivation? 😊

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5 Related Questions:

1. How would the EMI change if the interest rate were 12% instead of 10%?
2. What would be the total repayment Arjun makes over 3 years?
3. How is the EMI formula derived mathematically?
4. What is the difference between simple and compound interest in this context?
5. How does the compounding period (e.g., monthly vs annually) affect the EMI?

Tip:

Always check if the interest rate is compounded annually, semi-annually, or monthly, as it affects the calculation significantly!