To calculate the monthly installment $EMI$, we use the formula for Equated Monthly Installments:

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

Where:

• $P$ is the loan amount: ₹ 5,00,000
• $r$ is the monthly interest rate: $\frac{15}{12} \% = 0.0125$ (as a decimal)
• $n$ is the total number of months: $12$

Step 1: Substitute the values in the formula:

$EMI = \frac{500000 \cdot 0.0125 \cdot (1.0125)^{12}}{(1.0125)^{12} - 1}$

Step 2: Use the given value of $(1.0125)^{12} = 1.16075452$:

$EMI = \frac{500000 \cdot 0.0125 \cdot 1.16075452}{1.16075452 - 1}$

Step 3: Simplify the numerator:

$500000 \cdot 0.0125 \cdot 1.16075452 = 7254.71575$

Step 4: Calculate the denominator:

$1.16075452 - 1 = 0.16075452$

Step 5: Divide the numerator by the denominator:

$EMI = \frac{7254.71575}{0.16075452} \approx 45126.34$

Final Answer:

The monthly installment $EMI$ that Vipul has to pay is approximately ₹ 45126.34.

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Would you like further clarifications or detailed steps for better understanding? 😊

Relative Questions:

1. How does increasing the loan amount affect the EMI?
2. What happens to the EMI if the interest rate decreases to 12% p.a.?
3. How is the total interest paid over the loan term calculated?
4. Can we derive the same EMI using alternative methods like Excel formulas?
5. How would an increase in the tenure affect the EMI for the same loan?

Tip:

When calculating EMIs, breaking the formula into small steps (like handling powers and divisions separately) can help minimize calculation errors!