A man takes a personal loan of ₹ 2,00,000 at an interest rate of 15% p.a. compounded monthly, to be repaid by equal monthly instalments in 4 years. Calculate the EMI, using reducing balance method. [Given : $(1 \cdot 0125)^{-48} = 0 \cdot 55$ ]

Answer: The EMI is approximately ₹ 5555.55.

Step-by-step solution

Step 1: Identify Given Values

First, we identify the principal amount ( $P$ ), the monthly interest rate ( $r$ ), and the total number of monthly installments ( $n$ ). The annual interest rate is 15%, so we divide by 12 to get the monthly rate. The loan duration is 4 years, so we multiply by 12 to get the total number of months.

Step 2: Apply EMI Formula

We use the formula for calculating EMI (Equated Monthly Installment) for a loan based on the reducing balance method. This formula takes into account the principal amount, the monthly interest rate, and the total number of installments.

Step 3: Substitute Values into Formula

Now, we substitute the identified values of $P$ , $r$ , and $n$ into the EMI formula. This sets up the equation for calculation.

Step 4: Simplify the Expression

We simplify the terms inside the formula. We know that $(1+0.0125)$ is $1.0125$ . We are given that $(1.0125)^{-48} = 0.55$ . To use this, we can rewrite $(1.0125)^{48}$ as $1 / (1.0125)^{-48} = 1 / 0.55$ .

Step 5: Calculate $(1.0125)^{48}$

Using the given value, we calculate $(1.0125)^{48}$ by taking the reciprocal of $0.55$ . This gives us approximately $1.81818$ .

Step 6: Complete the EMI Calculation

Now, we substitute the calculated value of $(1.0125)^{48}$ back into the EMI formula and perform the final arithmetic operations to find the EMI.

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A man takes a personal loan of ₹ 2,00,000 at an interest rate of 15% p.a. compounded monthly, to be repaid by equal monthly instalments in 4 years. Calculate the EMI, using reducing balance method. [Given : (1⋅0125)−48=0⋅55(1 \cdot 0125)^{-48} = 0 \cdot 55(1⋅0125)−48=0⋅55]